National Aeronautics and

Space Administration

Langley Research Center

Hampton, Virginia 23681-2199

NASA/CR-2001-210869

Semiannual Report

October 1, 2000 through March 31, 2001

ICASE

NASA Langley Research Center

Hampton, Virginia

Operated by Universities Space Research Association

May 2001

Prepared for Langley Research Center

under Contract NAS1-97046
CONTENTS

Page

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Research in Progress

Applied and Numerical Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Computer Science .................................................................................. 9

Fluid Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Structures and Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Reports and Abstracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Interim Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Other Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Patents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Colloquia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Other Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Sta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

i
INTRODUCTION

ICASEis operated at the Langley Research Center (LaRC) of NASA by the Universities Space Research

Association (USRA) under a contract with the Center. USRA is a nonprot consortium of ma jor U.S. colleges

and universities.

The Institute conducts unclassied basic research in applied mathematics, numerical analysis and algorithm development, computer science, 
uid mechanics, and structures and materials in order to extend and

improve problem-solving capabilities in science and engineering, particularly in the areas of aeronautics and

space research.

ICASE has a small permanent sta. Research is conducted primarily by its permanent sta and visiting

scientists from universities and industry who have resident appointments for limited periods of time as well

as by visiting and resident consultants. Members of NASA's research sta may also be residents at ICASE

for limited periods.

The ma jor categories of the current ICASE research program are:  Applied and numerical mathematics, including multidisciplinary design optimization;  Applied computer science: system software, systems engineering, and parallel algorithms;  Theoretical, computational, and experimental research in 
uid mechanics in selected areas of interest

to LaRC, such as transition, turbulence, 
ow control, and acoustics; and

 Theoretical, computational, and experimental research in structures and material sciences with

emphasis on smart materials and nanotechnologies.

ICASE reports are primarily considered to be preprints of manuscripts that have been submitted to

appropriate research journals or that are to appear in conference proceedings. A list of these reports for the

period October 1, 2000 through March 31, 2001 is given in the Reports and Abstracts section, which follows

a brief description of the research in progress.



ICASE is operated at NASA Langley Research Center, Hampton, VA, under the National Aeronautics and Space Administration, NASA Contract No. NAS1-97046. Financial support was provided by NASA Contract Nos. NAS1-97046, NAS1-19480,

NAS1-18605, NAS1-18107, NAS1-17070, NAS1-17130, NAS1-15810, NAS1-16394, NAS1-14101, and NAS1-14472.

ii
RESEARCH IN PROGRESS

APPLIED AND NUMERICAL MATHEMATICS

Active 
ow control research tool development

Brian G. Al lan

The use of secondary 
ow control devices on inlets, such as vortex generators and small synthetic jets,

has recently attracted interest. Signicant improvements in engine 
ow distortion and pressure loss have

been demonstrated using these small 
ow control devices. This technology has shown a great potential for

improving existing inlet congurations and enabling more advanced inlet designs, allowing for reduced inlet

lengths and sharper turning angles. In order to take advantage of these devices, computational tools need

to be developed in order to evaluate potential engine inlet designs. The goal of this research is to develop

computational boundary conditions and techniques for a CFD code, in order to model vortex generators and

synthetic jets for inlet applications.

Using a compressible Navier-Stokes code developed at NASA, numerical simulations of micro-vortex

generators and vortex generator jets on a 
at plate and ramp have been performed. These simulations are

being followed by wind tunnel experiments conducted at NASA LaRC. The wind tunnel experiments will be

used to validate the numerical simulations of the vortex generators. From these simulations and experiments,

a better understanding of the 
ow physics of the 
ow control devices will be gained. Using these insights

into the 
ow physics of the control devices, a computational boundary condition can then be developed.

The goal is for the boundary condition to capture the general behavior of the 
ow control devices without

having to simulate them directly. This will result in a reduced computational cost by eliminating the need

to include ne grids for the vortex generators and synthetic jets. By reducing the computational cost, the

inlet design cycle time can also be signicantly reduced.

Future work will include a comparison of the numerical results to experimental data for a better understanding of the 
ow physics of these devices. Once an understanding of the 
ow physics is known, the

development of computational boundary conditions, which model the 
ow control devices, can be performed.

This work was done in collaboration with Pieter Buning (NASA Langley) using the ICASE PC cluster,

Coral.

Nonlinear suboptimal feedback control

Scott C. Beeler

Feedback control of nonlinear systems of ODEs is an area in which many methods have been proposed.

An optimal feedback control solution is usually impossible for nonlinear systems, so various suboptimal

approaches are used. These techniques can be applied to aircraft guidance and control problems including

abort-type scenarios and control eector impairment situations. This work will focus on the development

and study of suboptimal feedback control methods for problems of this type involving nonlinear dynamics

and control inputs.

We have begun studying the methods of dynamic inversion and the state-dependent Riccati equation

(SDRE) for feedback control. A preliminary version of the SDRE algorithm has been implemented for the

nonlinear-dynamics-and-input systems we are interested in, and the code is being tested and modied. Early

results show promise that further development of the method will produce desirable algorithm performance.

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Future eorts will work on modications to the SDRE method to improve its eectiveness and implementation of the dynamic inversion method (and possibly others) in code as well. The performance, stability, and

robustness of the methods used will be studied. Application of these control techniques to aircraft guidance

models is also planned for the future.

This work is done in collaboration with D. Moerder (NASA Langley).

Textbook multigrid eciency for CFD simulations

Boris Diskin

A multigrid method is dened as having textbook multigrid eciency (TME) if the solutions to the

governing system of equations are attained in a computational work that is a small (less than 10) multiple of

the operation count in one target-grid residual evaluation. The way to achieve this eciency for the Reynoldsaveraged Navier-Stokes (RANS) equations is the distributed relaxation approach separating dierent factors

contributing to the system and treating them optimally. The design of a distributed relaxation scheme

can be signicantly simplied if the target discretization possesses two properties: (1) The discretization

of the corresponding principally linearized system is factorizable, i.e., the determinant of the principal part

of the discrete matrix operator can be represented as a product of discrete scalar factors, each of them

approximating a corresponding factor of the dierential matrix operator determinant. (2) The obtained

scalar factor discretizations re
ect the physical anisotropies and are eciently solvable. In the last six

months, the research has been focused on deriving and analyzing new factorizable schemes and extending

TME to conservative discretizations of the Euler equations.

A collocated-grid scheme using second-order central dierencing for the pressure gradient and the velocity

divergence has been explored. The scheme being applied for compressible Euler system is factorizable in multiple dimensions. A typical diculty associated with this type of scheme is a poor measure of h-ellipticity

in the discrete approximation for the full-potential factor of the system determinant. A mechanism allowing

to improve the h-ellipticity measure by obtaining any desired discretizations for the full-potential factor of

the system determinant without compromising the scheme factorizability has been developed. The derived

h-elliptic factorizable discretization has been analyzed and tested.

A direct correspondence between the primitive variable interpolations for calculating 
uxes in conservative nite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation

has been established. Based on this correspondence, we have arrived at a conservative discretization that

is very eciently solved with a multigrid method involving a distributed relaxation scheme based on a

nonconservative formulation. TME has been demonstrated for conservative discretization of the quasi-onedimensional Euler equations.

A review summarizing the progress and outlining a road map for achieving TME for general problem

governed by RANS equations has been prepared.

Currently eorts are directed to demonstrate TME for multidimensional applications including general

boundary conditions and captured shocks.

This research is conducted in collaboration with J.L. Thomas (NASA Langley) and A. Brandt (The

Weizmann Institute of Science).

High-order unstructured grid methods for conservation laws Jan Hesthaven

The increasing emphasis on the modeling of unsteady problems over very long times and in computationally very large domains requires that accurate and ecient high-order methods be developed for such

2
problems. The geometric complexity, however, of problems of scientic and industrial interest makes such

developments a very signicant challenge. Unfortunately, the use of high-order/spectral methods, which

seems natural due to their superior numerical properties for wave propagation and their highly ecient

discretization of large computational domains, such methods have traditionally been restricted to domains

that can be smoothly mapped to a unit cube, thus allowing for the construction of a well-behaved multidimensional approximation using tensor products. As is well known, however, automated grid generation

and adaptive meshing is greatly complicated by using only hexahedrals as the fundamental element in a

general curvilinear multi-element formulation.

In a long-term eort to address and, eventually, overcome these restrictions we have continued the de- velopments of accurate high-order/spectral methods on triangles and tetrahedra. One of the novel aspects

of this eort is the representation of the approximate solutions using truly multi-variate Lagrange interpolation polynomials much in the spirit of classical spectral collocation methods, resulting in highly ecient

and simple implementations. The conservation law itself is satised in a weak sense, with the boundary

conditions only weakly through a penalty term. As we have shown recently, such formulations are highly

general, 
exible, and robust and lend themselves well to analysis of conservation and convergence as well as

highly ecient parallel implementations.

We have recently completed a thorough testing of a fully functional framework for the solution of threedimensional conservation laws with particular emphasis being paid to Maxwell's equations and scattering

and penetration applications. This successful testing period paves the way for the continuation of the eort

to address techniques for handling strong shocks, ecient time-advancement, and, eventually, space-time

adaptivity for geometrically complex three-dimensional problems.

This is a collaborative eort, involving David Gottlieb and members of the Electromagnetics branch at

NASA Langley. Robust optimization including model uncertainties and reliability constraints

Luc Huyse

During the preliminary design stages only crude estimates are known for many model parameters in a

particular problem. Deterministic optimization using these tentative parameter values can lead to overly

optimistic pro jections of the as-built performance. It is quite typical for the optimal design to be fairly

sensitive to 
uctuations in model parameters. This research develops statistical optimization methods that

directly account for parameter uncertainty.

In our formulation we model the uncertainties explicitly as random variables. Based on the statistical

decision theory we developed a theoretical framework for robust (or stochastic) optimization. The ob jective of

robust optimization is to nd the design with the best lifetime performance. Using analytic approximations

of the stochastic integral we were able to formulate a new deterministic equivalent problem (DEP). The

optimization of the DEP requires higher-order derivatives but provides additional insight in the problem.

We also developed a new algorithm for the full integration of the stochastic integral. Careful analysis thereof

has revealed the superiority of this method over traditional multi-point design. Statistical decision theory

provides a theoretical basis for the selection of the design conditions and their respective weights in the

overall ob jective function.

The newly developed techniques were applied to an airfoil optimization problem, using NASA Langley's

FUN2D code. The minimization of the drag in cruise regime while maintaining a constant lift is chosen as the

ob jective function. Only the Mach number is assumed to be uncertain in this demonstration problem. The

3
approximate second-order formulation leads to a considerable improvement of the robustness when compared

to a deterministic single-point design. We also compared the results of the new stochastic integration

algorithm to traditional multi-point design using an optimal set of weights. Our experience has been that

the new algorithm is capable of drastically reducing the so-called \drag-troughs." The ultimate goal is to

develop general-purpose robust optimization methods for use in multidisciplinary design.

This work was conducted in collaboration with Sharon Padula (NASA Langley). The researchers are

indebted to Wu Li (Old Dominion University) for his parallelization eorts of our modications to NASA's

FUN2D code.

The Coral Pro ject

Josip Loncaric, Thomas W. Crockett, Piyush Mehrotra, Peter Kearney, and Manuel D. Salas

The cost of developing complex computer components such as CPUs has become so high that scientic

applications alone cannot carry the full burden. In the future, scientic computing will have to use mass

market leverage to overcome the cost barrier. A cost-eective alternative to high-end supercomputing was

pioneered by Beowulf, a cluster of commodity PCs. By now, high performance Beowulf clusters can be built

using fast commodity PCs and switched Fast Ethernet. We are exploring the benets and the limitations of

this approach, based on applications of interest to ICASE.

The initial phase of the Coral pro ject, consisting of 32 Pentium II 400 MHz nodes and a dual-CPU

server, demonstrated aggregate peak performance in excess of 10 G
op/s, with sustained performance on

CFD applications of about 1.5 G
op/s. In order to provide a richer environment for further experimentation,

a dual-CPU conguration was chosen for the second phase of the Coral pro ject. We have added 16 dual

Pentium III 500 MHz machines and two dual-CPU le servers. The third stage of this pro ject added 16 dual

Pentium III 800 MHz machines and a 32-node low latency 1.25 Gbps Giganet cLAN network fabric. The

resulting system contains 96 compute CPUs with an aggregate of 36 GB of RAM and 981 GB of local disk

space. Coral's three dual-CPU servers provide an additional 1.5 GB of RAM and 246 GB of disk space.

Coral has an excellent price/performance ratio, almost an order of magnitude better than an equivalent

proprietary supercomputer design. This conclusion is based on our experience with a variety of applications,

ranging from coarse-grained domain decomposition codes to communication-intensive parallel renderers.

Extensive testing of MPI performance using LAM, MPI/Pro, MPICH, and MVICH libraries over TCP

(Fast Ethernet) and VIA (Giganet cLAN) transports was completed in October 2000. The measurements

reveal signicantly lower MPI latency of polling implementations although interrupt driven receive can

overlap computation and communication and thus, deliver higher performance in some applications.

To monitor Coral's performance, we wrote our own cluster node monitor utility whose main benet is

extremely low overhead and the ability to monitor Giganet cLAN trac.

The Coral cluster usage has dramatically increased this year. Since October of 2000, Coral's 102 CPUs

delivered 19,527 CPU*hours of computing per month on the average. We will continue to use this cluster to

develop and run research codes of interest to ICASE and NASA Langley, and to evaluate price/performance

tradeos among various hardware, software, and networking congurations.

Active shielding and control of environmental noise

Josip Loncaric, Victor S. Ryaben'kii, and Semyon V. Tsynkov

Rejection of exterior noise caused by periodic sources such as propellers or turbines would signicantly

enhance passenger comfort and reduce noise fatigue on long 
ights. Passive sound absorbing materials help at

high frequencies, but to be eective below about 1 kHz their weight penalty becomes signicant. Active noise

4
control can reduce low frequency noise with less weight penalty. Based on the mathematical foundations of a

new active technique for control of the time-harmonic acoustic disturbances, we are developing a numerical

technique that will suggest good locations for sensors and actuators.

Unlike many existing methodologies, the new approach provides for the exact volumetric cancellation

of the unwanted noise in a given predetermined region of space while leaving those components of the total

sound eld deemed as friendly unaltered in the same region. Besides, the analysis allows us to conclude that

to eliminate the unwanted component of the acoustic eld in a given area, one needs to know relatively little:

only the perimeter data (the total acoustic eld and its normal derivative) are required. The mathematical

apparatus used for deriving the general solution is closely connected to the concepts of generalized potentials

and boundary pro jections of Calderon's type. This exact general solution can be computed at polynomial

cost, and good actuator locations determined via a procedure which progressively restricts the locations

where actuators may be placed. While the actuator placement problem is still computationally challenging,

this approach is much more ecient than the alternatives, which lead combinatorial computational cost. We

are in the process of developing a numerical procedure that reduces the number of candidate locations based

on the minimization of the control eort.

In order to develop numerically computable solutions, we intend to describe the discrete framework for

the noise control problem parallel to the continuous one. This discrete framework is obtained using dierence

potentials method; in the future it is going to be used for analyzing complex congurations that originate

from practical designs. Once we have computed the solution for a particular conguration, we intend to

investigate the possibilities of optimizing it according to the dierent criteria that would t dierent practical

requirements. We expect to discuss the applicability of the technique to quasi-stationary problems, future

extensions to the cases of the broad-band spectra of disturbances, as well as other possible applications

which may include dierent physics, such as electrodynamics, and dierent formulations of the boundary- value problems, such as scattering.

Large-eddy simulation using a parallel multigrid solver Dimitri J. Mavriplis

The failure to develop a universally valid turbulence model coupled with recent advances in computational technology have generated a greater interest in the large-eddy simulation approach for computing 
ows

with large amounts of separation. This approach involves resolving the large-scale unsteady turbulent eddies

down to a universally valid range in the hope of yielding a more generally valid simulation tool. The purpose

of this work is to develop a large-eddy simulation capability based on an existing unstructured grid NavierStokes solver. The use of unstructured grids, which facilitates the discretization of complex geometries and

adaptive meshing techniques, is expected to enhance the 
exibility of the resulting simulation capability. An unsteady Reynolds-averaged Navier-Stokes (RANS) 
ow solver based on unstructured meshes has

been developed and validated on the case of a circular cylinder. A Detached Eddy Simulation (DES) model

based on modications to the one-equation Spalart-Allmaras RANS turbulence model has been implemented

and validated for the case of 
ow over a sphere. Isotropic decaying turbulence has been simulated on grids of various resolutions and comparisons of the decaying turbulence spectra with experimental results has been

made. These results emphasize the eect articial dissipation can have on the turbulence spectra and are

currently being used to provide guidelines for the maximum permissible levels of dissipation for properly

capturing the inertial range of turbulence scales. These computations are being performed on the ICASE

PC cluster, Coral.

5
Higher resolution simulations are currently underway as well as simulations for a stalled wing and 
ow

over a blu landing-gear geometry. This work is being carried out in collaboration with Juan Pelaez (Old Dominion University).

Linear and nonlinear unstructured multigrid algorithms for the solution of radiation hydrodynamic problems

Dimitri J. Mavriplis

Under the ASCI program, the simulation of radiation transport and hydrodynamic phenomena have

been identied as one of the most time-consuming elements within large simulation codes. The ob jective of

this research is to investigate the relative benets of unstructured multigrid algorithms used as linear solvers,

nonlinear solvers, or preconditioners in eciently solving unsteady radiation hydrodynamics problems, in

the radiation diusion limit.

A linear version and a nonlinear version of an agglomeration multigrid algorithm have been developed and

applied to the two-dimensional radiation diusion system, and the two-dimensional Navier-Stokes equations,

both as solvers directly, and as preconditioners for a Newton-Krylov method.

Theoretical and numerical evidence is given which shows the equivalence of the linear and nonlinear multigrid methods in the asymptotic convergence region, in terms of multigrid cycles. However, for complex

nonlinear operators, the linear multigrid approach provides lower cost multigrid cycles and therefore results

in a more ecient algorithm. In cases where an inexact linearization is employed, overall solution eciency

is determined by the cost of a linear versus a nonlinear multigrid cycle, and the numerical convergence

eectiveness of the inexact linear system. In such cases, using the linear or nonlinear multigrid methods as

preconditioners to a Newton-Krylov method can result in large gains in eciency. These results are to be extended into the three-dimensional setting and eects of scalability on large numbers of processors will be studied in addition to algorithmic eciency. A complete validation of the

solver in terms of accuracy will also be completed in the near future.

Linear parameter varying control of an aircraft under adverse conditions

Jong-Yeob Shin

Recent aircraft 
ight control design research has concentrated on the development of control systems

that stabilize an aircraft robustly and allow to recover aircraft performance under adverse conditions (actuator/sensor/engine failures and bad weather). One promising approach to designing robust 
ight control

systems (FCS) for an aircraft under adverse conditions is use of linear parameter varying (LPV) control

synthesis, since aircraft dynamics vary signicantly according to angle of attack, velocity, dynamic pressure,

and so on. Aircraft dynamics can be described by a quasi-LPV model with scheduling parameters, which

are also states of the dynamics model.

We have currently formulated a quasi-LPV model of aircraft dynamics including longitudinal and lateraldirectional axes by a function substitution method that uses linear programming optimization. In order to

apply LPV control synthesis for designing a robust FCS, a quasi-LPV model of aircraft dynamics, and a

model of aircraft at failure cases are required. We are currently investigating control surface failure cases

and preliminary dynamic models to facilitate possible failures.

In future work, failure cases will be parameterized and integrated into LPV controller synthesis for

an aircraft FCS. Due to an increasing number of scheduling parameters in LPV controller synthesis for

actuator and/or sensor failure cases, blending approach of LPV controller synthesis is required to develop

6
an LPV controller that stabilizes an aircraft robustly under adverse conditions and also minimizes aircraft

performance degradation.

This research was conducted in collaboration with Christine Belcastro (NASA Langley).

High-order discontinuous Galerkin method and WENO schemes

Chi-Wang Shu

Our motivation is to have high-order non-oscillatory methods for structured and unstructured mesh that

are easy to implement for parallel machines. The ob jective is to develop and apply high-order discontinuous

Galerkin nite element methods and weighted ENO schemes for convection-dominated problems. The applications will be problems in aeroacoustics and other time-dependent problems with complicated solution

structure.

Jointly with Harold Atkins at NASA Langley, we are continuing in the investigation of developing the

discontinuous Galerkin method to solve the convection-dominated convection-diusion equations. We have

been continuing in our investigation of local preconditioners coupled with multigrid, which hopefully would

dramatically increase the eciency of time stepping for time-dependent simulations and make convergence

to steady states faster, both for convection problems and for convection-diusion problems. Jointly with

Jue Yan, we have been developing a local discontinuous Galerkin method for KdV-type equations containing

third derivative terms. The scheme is especially suitable for problems containing nonlinear rst derivative

terms and a linear or nonlinear term with small coecients.

Research will be continued for high-order discontinuous Galerkin methods and weighted ENO methods

and their applications.

Linear programming approaches to potential function modeling for protein folding

Michael Wagner

The protein folding problem is one of the grand challenges in computational science. The recent unveiling

of the human genome and the conclusion that the number of human genes is much smaller than originally

thought makes the study of proteins, their function, and interactions even more important. Our eort

focuses on nding good models for the energy (or potential) function that drives the folding process of

proteins. There are a variety of dierent functional models that require the knowledge of certain parameters

that appear linearly. We use linear programming to nd these parameters so that the model predicts the

structure of known proteins in the publicly available databases correctly. This model can then be used for

structure recognition for unknown sequences or for ab-initio folding.

The resulting linear programming problems have a few hundred variables, tens (possibly hundreds) of

millions of constraints and a completely dense constraint matrix and are, thus, rather challenging to solve.

By exploiting LP duality theory and the structure of the problem we are able to tackle these problems

by adapting the interior point solver PCx (by Czyzyk, Mehrotra, Wagner and Wright, Argonne National

Lab). We use dense parallel linear algebra and a streamlined interface to Loopp (by Elber and Meller, Cornell

University), the software that generates the data. We were able to solve problems with ten million constraints

in 300 parameters in a few hours on 48 nodes of the Intel Pentium PC-based Velocity Cluster at the Cornell

Theory Center. Details of the results were presented at the SIAM Conference on Parallel Processing in

Portsmouth, VA in March of this year, a paper was submitted to the Journal of Computational Chemistry. A second, more technical writeup is in progress and will be submitted to a computational optimization

journal.

7
Future work will include optimizing the code to allow for even larger scale problems. We believe that

solving problems with 50 million constraints is well within our reach, scaling up by another order of magnitude

is the next step. We are in the process of testing dierent functional models, the approach holds much promise

to the computational chemists and biologists in the group. Finally, we are in the process of adapting the

parallel LP solver to allow for the ecient solution of general LPs. Given time we will develop a version of

the algorithm that is entirely independent of the underlying data structures and BLAS implementation.

This is joint work with Jarek Meller and Ron Elber (Cornell Computer Science Department).

8
COMPUTER SCIENCE

Preconditioning techniques for solving the particulate 
ow problem in parallel

Abdelkader Baggag

To extract the implicit information that is in the equations of the motion of the particulate 
ow problem,

it is necessary to numerically solve the coupled system of PDEs consisting of the equations of the 
uid

motion, and the equations of the rigid-body motion (governing the particle motions). These equations are

coupled through the no-slip boundary condition on the particle surfaces, and through the hydrodynamic

forces and torques exerted by the 
uid on the particles. To solve it numerically, the particulate 
ow problem

is discretized by a standard Galerkin nite element scheme, in which both the 
uid and particle equations

of motion are incorporated into a single variational equation where the 
uid and particle velocities appear

as primitive unknowns. The computation is then performed on an unstructured grid, and an arbitrary

Lagrangian-Eulerian moving mesh technique is adopted to deal with the motion of the particles.

The numerical simulation of the particulate 
ow problem is extremely computationally intensive, since

it is nonstationary, i.e., it evolves over many time steps, and within each time step a nonlinear system of

equations must be solved, and within each nonlinear iteration several linear systems are solved. The time

stepping is handled by a backward Euler scheme, and a Newton method is used to deal with the nonlinearity. The various algebraic systems (Jacobians) that arise thereafter are large, sparse, nonsymmetric, and often

indenite, and their solution can consume up to 90% of the total CPU time of the entire simulation. The

main focus of this research is to address the ecient solution of the linear systems and to implement them

on parallel computers, and to optimize them in particular on the Origin 2000.

Although the methods based on the Krylov subspaces have excellent parallelization properties, they

lack robustness without good preconditioning. In this research some novel techniques are investigated and

devised. These techniques include the balance scheme, the multilevel method, and the augmentation method.

These algorithms are implemented in a Particle Mover ob ject-oriented code, called PM++, and extensively

validated for the particulate 
ow problem of the Grand-Challenge pro ject.

This research was conducted in collaboration with Ahmed Sameh (Purdue University).

Nautilus problem solving environment (PSE)

Thomas M. Eidson

Programming eciency has been a problem in the scientic community for many years. Attempting to

extract good performance from state-of-the-art high-performance architectures can be very time consuming.

The rapid changes in computing environments has inhibited the development of standards and synergetic

tools. Distributed computing, especially on Grids, makes the situation worse as heterogeneous computing

environments at multiple sites necessitate that an enormous amount of detail must be managed by the programmer. The situation is further complicated by the fact that larger, composite applications are becoming

more common. The Nautilus Pro ject will provide a PSE implementation both to study various PSE design

issues related to programming composite applications and to provide a framework for ICASE and NASA

pro jects to experiment with application development using a Grid/distributed programming model.

The Nautilus PSE is targeted for usage by scientic application developers who work with researchoriented applications. The programming model for Nautilus will be based on component programming

concepts. Currently, the evolving specication being developed by the Common Component Architecture

9
(CCA) Forum is being targeted. The Nautilus design is a combination of concepts from the LAWE System

(a prototype previously developed via a NASA SBIR) and concepts from the CCA Forum. A number of

prototypes are under development that are being used to support the CCA specication development. Several

of these prototypes are being studied for possible use as the starting point for the Nautilus development. The

Nautilus design extends these basic CCA implementations to provide a richer, intuitive set of programming

abstractions so that more sophisticated distributed applications can be developed. The Nautilus design

also provides a more complete set of tools, in particular, to support the programming style of the research

scientist. A rst phase Nautilus design has been completed and a paper is being written to describe the

concepts and details of that design. Two CCA prototypes, CCAFFEINE and CCAT, are being installed.

First, CCAFFEINE and CCAT will be studied and application developers will be recruited to use and

to evaluate these programming frameworks. Because these prototypes are developed in a component style,

the goal is to evolve one of these prototypes to the Nautilus design by gradually replacing its components.

Interaction with the Grid Forum and the CCA Forum will continue so that Nautilus will include compatibility

with any new standards or technology in the area of scientic PSEs for Grid computing.

Shared programming denition (SPD) pro ject

Thomas M. Eidson

A number of Problem Solving Environments (PSE) for creating distributed applications on heterogeneous

networks are under development. While many of these PSEs have similarities, such as a component-like

design, they each target dierent application and user needs and they generally use dierent programming

models. Since distributed applications are often composed of or developed from applications created in local

environments, a degree of consistency across these dierent programming domains will aid code transfer.

While some diversity is desired to meet the variety of dierent needs, application developers will benet from

some degree of homogeneity in the design and use of dierent PSEs.

The Advanced Programming Models Working Group (APM) of the Grid Forum is chartered with the

general task of recommending standards for Grid programming. A ma jor focus of this group has been on

component-based PSEs and on understanding the similarity and dierences between the various existing

research prototypes. Currently, a pro ject, led by this author, is underway to gather information in a format

to support a more detailed comparison of these prototypes. As a separate eort, an ICASE/NASA Workshop

on Grid Programming has been planned for April 12 and 13 to further investigate Grid programming. A small

group of PSE developers with expertise in a diverse set of approaches have been invited. The format will be

to discuss relevant topics with the goal of formulating a suggested approach (possibly a pro ject to recommend

to NASA) to address issues such as the need for standards to support portability and interoperability of

applications across dierent PSEs. A proposal for Shared Programming Denitions has been developed that

has/will be discussed with both of the above groups.

Work with the Grid Forum will continue with the goal of developing standards for PSEs to support

programming eciency. The results of the rst workshop will be formulated into a report and a presentation.

A second workshop will be organized where these results are presented to and discussed with NASA personnel.

Tidewater Research Grid Pro ject (TRGP)

Thomas M. Eidson

A recent trend in scientic computing has been the increased use of Grid computing. Grid computing

is dened as the development and execution of distributed applications across wide-area networks where administrative and security issues are non-trivial. Very high-performance computers have become increasingly

10
expensive and researchers are looking to the use of large numbers of lower-performance machines to meet

their computational needs. Unfortunately, these machines are located at various locations where the Internet

(or an internet) is involved, thus the need for Grid computing. The Globus Pro ject (Argonne National Lab

and ISI Lab of Univ. of Southern California) has developed the Globus Toolkit to provide core services to

run a computational Grid.

The TRGP is a pro ject to set up a computational Grid for ICASE access. Currently, the other member

organizations include labs from Old Dominion University and The College of William & Mary. A preliminary

installation of the Globus Toolkit has been installed and tested at ICASE. Several meetings with representatives from member organizations have been held to agree on policies. This included the use of PGP to

provide a system of trusted communication between the various organizations who are physically distributed.

June 2001 has been set as a target date for initial operation.

A nal installation of Globus must be completed. Communication, account management, and other

procedures must be nalized. Documentation must be completed. Once these steps are done, the TRGP

will be made available to the member organizations. Joint pro jects that use multiple sites will need to be

encouraged as the success of such pro jects will be the measure of the success of the TRGP. Verication of air trac management systems

Gil les Dowek, Alfons Geser, and Cesar Mu~noz

Safety assessment of new air trac management systems is a main issue for civil aviation authorities.

Standard techniques such as testing and simulation have serious limitations in new systems that are signi-

cantly more autonomous than the older ones. The aim of this work is to develop formal techniques to verify

the correctness of systems and concepts developed under the Distributed Air/Ground Trac Management

(DAG-TM) pro ject at NASA.

Avionics systems are particularly dicult to verify because of their hybrid nature: they involve at the

same time continuous behaviors, e.g., aircraft tra jectories, and discrete ones, e.g., logical control. We have

developed a continuous model of aircraft tra jectories that is well suited for formal verication. The model

consists of a mathematical model of the dynamics of an aircraft based on physical laws of kinematics and a

set of theories dealing with standard calculus and continuous mathematics. Model and theories are written

in the specication language of PVS. An alerting algorithm for parallel landing has been proved correct using

this model. Using the same approach, we have discovered a new algorithm for tactical con
ict detection and

resolution (CD&R) in a three-dimensional space.

In the near future, we will formally prove the correctness of our CD&R algorithm. We will also integrate

it into a more general system for strategic CD&R, which takes into account intent information such as 
ight

plans and uncertainties such as weather conditions.

Verication of the SPIDER protocols

Alfons Geser

Systems that are used in safety-critical applications must be highly dependable. Communication between

electronic equipment in such a system is particularly sensitive. For instance it is required that message

exchange must not fail more than once per as much as 120,000 years. In order to arrive at such a high level

of condence, the communication hardware must operate without failure in the presence of various kinds of

faults, including simultaneous faults and Byzantine faults that can exhibit a malicious, two-faced behavior.

In order to avoid design errors to an extent possible by today's means, the hardware including its fault

tolerance mechanism has to be formally veried.

11
The SPIDER architecture is designed to serve as a fault tolerant message exchange backbone between

unreliable nodes of electronic equipment. For this purpose it consists of nodes that tolerate faults of each

other. SPIDER has an Interactive Consistency Exchange Protocol that ensures correct transmission from

good nodes to good nodes, and ensures equal views of the scenario among all good nodes. A Diagnostic

Protocol must gather information about misbehavior of nodes, and exchange that information such that all

good nodes arrive at an equal, correct judgment of the quality of each node.

Using a given formal verication of the Interactive Consistency Protocol, we have started and nearly

nished a formal verication of the Diagnostic Protocol in PVS. We plan next to participate in the design of

the Initialization Protocol, a critical phase where the nodes have to nd a common timing before they can

start working.

Scalable implicit solvers for PDEs and PDE-constrained optimization

David E. Keyes

The development of scalable implicit solvers for analysis and optimization of multiscale phenomena

governed by PDEs are our chief ob jectives. Multilevel preconditioned Newton-Krylov methods, from twolevel additive Schwarz to richer versions, have proven to be broadly applicable, architecturally versatile, and

tunable for high performance on today's high-end commercial parallel platforms. The challenge of obtaining

high performance is likely to be increased on coming generations of high-end machines, as represented, for

instance, by the ASCI \white" machine at Lawrence Livermore National Laboratory, and also on Beowulf

clusters, such as ICASE's Coral. Our primary eorts are concentrated on algorithmic adaptations of matrixfree Newton-Krylov methodology appropriate for emerging architectures.

Since we employ Newton's method as the solver, we can also apply our techniques to nonlinear systems

that augment the original PDE discrete equations by additional equations that represent the rst-order

necessary conditions (the Karush-Kuhn-Tucker equations) for optimality. Working through the Lagrange

formulation for PDE-constrained optimization, we designate this approach Lagrange-Newton-Krylov. Both structured-grid and unstructured-grid CFD legacy codes have been ported to advanced platforms

and reasonable ob jectives for algorithmic convergence rate, parallel eciency, and raw 
oating point performance have been met. The general approach is documented in previous ICASE technical reports, among

other places. Newton's method, robustied by pseudo-transient continuation, generates global linear systems

that are solved in a matrix-free manner by Krylov iteration, and preconditioned locally. In the absence of

timestepping, a non-local two-level preconditioner based on a coarsening of the problem is also required

to maintain algorithmic scalability at a modest cost to asymptotic parallel eciency, but most nonlinear

problems require some form of timestepping, even for the computations of steady states.

During the past year, our 1999 Bell Prize-winning work | an implementation of the NASA code FUN3D

running on up to 3,072 dual-processor nodes of the ASCI Red machine at 227 Giga
op/s | has been extended

by algorithmic performance tuning and memory system modeling to the mid-300's of Giga
op/s, while we

await access to the next larger machine.

Domain-decomposition algorithms for PDEs and Lagrange-based algorithms for PDE-constrained optimization are special cases of partitioned solvers, where the partitions are geometrically or functionally based,

respectively. We are examining a variety of partitioned solvers, where the variety arises from the type of

partitioning and also the order of nestedness of the partitioning with respect to the linearization required

in any nonlinear problem. A key decision in the trade-o between globalized convergence properties and

parallel computational cost per iteration is whether a global Newton linearization is employed, or multiple

12
independent Newton linearizations within partitions.

We will continue to develop Newton-Krylov methods in implicit parallel CFD and radiation transport,

examining a variety of algorithmic, programming paradigm, and architectural issues.

One of the most exciting new areas is nonlinear additive Schwarz. This is a nonlinear preconditioning

that has already proved to enlarge the domain of convergence of a Newton's method wrapped outside of it,

in boundary layer and shocked duct 
ows. The cost is the concurrent solution of numerous smaller nonlinear

problems on subsets of the unknowns, and solution of linear problems on the same subsets to apply the action

of the preconditioned Jacobian. Besides robustication advantages, in the range of thousands of processors,

the nonlinear preconditioning has the potential to signicantly reduce the number of synchronization points,

by concentrating work locally. This research was being conducted in collaboration with Xiao-Chuan Cai (University of Colorado, Boulder), William Gropp, Barry Smith, and Paul Hovland (Argonne National Laboratory), Dinesh Kaushik and

Widodo Samyono (Old Dominion University), Carol Woodward (Lawrence Livermore National Laboratory),

and David P. Young (Boeing)

Heterogeneous specication formalisms for reactive systems

Gerald Luttgen

This research is part of the NSF pro ject CCR-9988489, which is devoted to the development of novel

techniques for heterogeneous formal specications of reactive systems, such as avionics systems and embedded

software. The pro ject might be seen as a response to the need that formal-methods research must start addressing multi{paradigm specications|combining, e.g., operational and assertional styles of specication|

in order to support the heterogeneous specication methodologies employed in engineering practice today. Recent and current research within the pro ject focuses on extending the process algebra Calculus of

Communicating Systems (CCS), that supports an operational style of specication, by two operators that

permit the inclusion of Linear-time Temporal Logic (LTL) formulas, thereby adding an assertional style of

specication. The two operators are:  embed (), where  is a LTL formula; this operator facilitates the embedding of LTL formulas within

process-algebraic terms.  constraint (P,), where P is a process term and  is a LTL formula; this operator allows one to

restrict the behavior of P as specied by . The resulting mixed language has been given an operational semantics based on Streett automata, in terms

of structural operational rules. Further, it has been investigated how exactly the notion of Buchi/Streett

testing, which was previously developed under ICASE/NASA funding, can be adapted to the novel setting. In

particular, the Buchi/Streett must-testing preorder would allow for an elegant theory supporting the stepwise

renement of assertional system requirements into operationally concrete system designs. Unfortunately, a

straightforward adaptation of the preorder to our language leads to a subtle compositionality defect regarding

parallel composition, which is currently under investigation. It should be noted that this basic research is a

prerequisite for a clean semantic support of heterogeneous specication languages and methods in use today. Regarding further work in the near future, it is planned to characterize the largest pre-congruence

contained in the Buchi/Streett must-testing preorder and to investigate concurrency-theoretic issues of the

resulting heterogeneous language.

The reported research was conducted in collaboration with Rance Cleaveland (SUNY at Stony Brook,

New York), the principal investigator of the NSF pro ject.

13
System software research plan

Merrel l Patrick

The overall ob jective of this research is to develop software that supports the development of leading

edge, large-scale distributed applications that run on networked heterogeneous computing systems. At the

highest level the central focus of the research is the programming of multidisciplinary applications and

application components in a way that not only supports ease of programming but also portability and

interoperability across dierent sets of networked systems. Portability and interoperability imposes the need

for development of standards for such programming languages and environments. Developing meaningful

standards that will have broad impact and be of use to NASA will require collaboration with national forums

and groups, researchers at universities and government labs, and commercial developers of frameworks,

compilers, toolkits, shells, and portals.

Programming requirements across various application areas are very diverse and varieties of programming

approaches have been or are being used. These range from (a) frameworks where software components are

combined to create applications to; (b) network-aware compilers that specialize in data-parallel and taskparallel applications to; and (c) simple work
ow programming systems such as shells, toolkits, and portals.

The ICASE systems software plan has been restructured to have an overarching focus on the development

of a higher level programming and execution framework (PEF) with appropriate standards that supports the

portability, interoperability, and scalability of integrated multi-disciplinary codes across networked computing systems. The development process will use abstractions drawn from the above mentioned approaches.

These abstractions will help dene standards to be used. This research will be done by ICASE at NASA

Langley in collaboration with working groups of the Grid Forum and the Common Component Architecture

Working Group. The ICASE team will work with NASA HPCC applications development teams and de- velopers of commercial products so as to better address NASA needs and the shortcomings of commercial

products. ICASE will develop a prototype PEF to test requirements as hypothesized by applications teams

and framework developers.

The overall plan includes three pro jects, an overarching pro ject focused on framework development and

two important components of the framework. The tasks are:

1. Development of a component-based Programming and Execution Framework (PEF) for distributed

applications.

The programming methodology of the system will be on software component principles to support

the quick development and modication of applications. Ma jor features include:  a scalable, distributed computing programming and execution support system that provides

state-of-the-art security and that includes the following features: { run-time resource discovery and resolution { process to resource run-time mapping { remote process management { remote task execution (in a task server process) { synchronizing event signals { data transfers for medium and high performance needs { remote le transfer management { execution steering { programming of host work
ow and remote application servers.

14
 a visual, component programming system using one or more technologies such as Web-based,

Java Beans.  a set of performance monitoring and diagnostic tools to assist in the development applications

codes which execute eciently on networked systems.  a set of executables and scripts that provide application development and execution support.  a set of standards-based, programming abstractions to dene the elements and work
ow of a

distributed application developed jointly with relevant standards groups.  a set variety of communication and information discovery technologies including Globus Services

and Java/Jini.

2. Development of data management component technologies for distributed scientic applications.

The focus is an XML-based data management software component to support scientic data portability across dierent programs on dierent machines, and exploration of scientic data with tools

not necessarily available locally. Both a human and program interface to the software facility is

planned. Technologies to be considered will include:  metadata for dening data sets  XISL (from CACR, Caltech), an XML-based standard to represent scientic data

 standard software components for transformation and exploring data sets  XSLT implementation such as Xalan-Java from Apache  use of extended XSL for specifying transformations.  systems and/or protocols for high-performance data transfers { stream programming

 \add-on" techniques to lter data transfers  aspect-oriented programming

 run-time data lters  systems and/or protocols for event management  publish/query programming

3. Developing language extensions for high performance and distributed computing.

Dierent language approaches will be evaluated and extensions and new compilation techniques that

support ease of programming while exploiting the power of parallel and distributed computers will

be proposed. OpenMP will be a primary focus.

The research proposed in the above pro jects is targeted at meeting the programming needs of future

NASA computational pro jects; in particular, designing complex space and aircraft systems. It is anticipated

that such pro jects will include a large set of multidisciplinary computational codes (stand-alone executables

as well as function libraries) that will interact using non-trivial communications. The research will address

improved user eciency. This will allow application developers and users to focus on quality of the physics

modeled by applications rather than on the computer science details of the programming environment.

During the last six months several meetings with LaRC applications developers have been held with the

goal of identifying computational framework requirements. Also a workshop involving researchers working in

frameworks, compilers, toolkits, shells, and portals has been planned and will be held in April 2001. A goal

is identify programming abstractions that can be used to dene standards for implementing programming

frameworks and to identify framework requirements as seen by the software developers.

The above pro jects are the joint eorts of T. Eidson (ICASE), M. Zubair (Old Dominion University and

ICASE), and Barbara Chapman (University of Houston and ICASE).

15
Scalable parallel algorithms for incomplete factorization preconditioning

Alex Pothen

The parallel computation of robust preconditioners is necessary for solving large systems of equations by

iterative methods. We are developing scalable parallel algorithms and software that can compute incomplete

factorization preconditioners for high levels of ll.

We create parallelism by partitioning the adjacency graph of the coecient matrix into subgraphs of

roughly equal sizes such that each subgraph has few boundary nodes relative to the number of interior nodes.

We preserve the parallelism in two steps: First, we map the subgraphs to processors, form a subdomain

interconnection graph, and order the subdomains by a graph coloring to reduce global dependences. Second,

on each subdomain, we locally reorder the interior vertices before the boundary vertices. This reordering

limits the ll that joins a subgraph on one processor to a subgraph on another: such ll edges join only

boundary vertices on one subgraph to boundary vertices on a neighboring subgraph.

We have earlier reported results on problem sizes of up to 20 million rows and columns on up to 216

processors of the SGI Origin, the Cray T3E, the Sun HPC 10000, and Coral, the ICASE Beowulf cluster.

We are currently implementing our algorithms on larger numbers of processors and applying them to other

classes of problems. We expect to show by these experiments that our algorithm is scalable, in agreement

with our analysis of the algorithm.

This is joint work with David Hysom (Old Dominion University, currently at Lawrence Livermore National Laboratory).

External memory sparse direct solvers Alex Pothen

We consider issues in designing external memory algorithms and software for solving large, sparse systems

of equations by means of direct solvers. Such methods will enable sparse direct solvers to make eective

use of the Gigabytes of memory and Terabytes of storage available on serial computers; parallel algorithms

running on PC clusters like Coral and Tera
op parallel computers with multiple levels of memory hierarchy

will also benet.

We formalize two problems for external memory sparse matrix factorizations: minimizing the primary

memory required in a read-once/write-once model, and minimizing the data movement needed in a readmany/write-many model. We compute bounds on these quantities for sparse model problems whose data

dependence graphs (elimination trees) have simple structures. We study the in
uence of orderings, factorization algorithms, and blocking on the primary memory requirements and the data movement costs of a sparse

factorization algorithm. The relative performance of the three commonly used variants of the factorization

algorithm, viz. left-looking, right-looking, multifrontal, and recursive, can vary by orders of magnitude for

unbalanced elimination trees that occur in linear programming and related applications. We have designed

fast simulators that compute the data movement costs of these algorithms in time proportional to the size

of the factors rather than the 
ops required to compute them.

We propose to extend OBLIO, our ob ject-oriented sparse direct solver library, with serial and parallel

implementations of external memory solvers.

This is joint work with Florin Dobrian (Old Dominion University).

16
Coloring graphs in parallel for optimization

Alex Pothen

Optimization algorithms that employ derivative information require the computation of a Jacobian or

Hessian matrix. Automatic dierentiation (AD) and nite dierences (FD) are two techniques used to

compute these matrices. It is well known that graph coloring algorithms could be used to reduce the number

of function evaluations needed in estimating the Jacobian and the Hessian. We have begun to develop parallel

algorithms for graph coloring applicable to optimization.

Our rst contribution is a unied perspective of the various graph coloring problems, corresponding

to Jacobian and Hessian estimation, and corresponding to FD or AD techniques. We show that all these

problems could be formulated as a single, albeit non-traditional, graph coloring problem. We extend a

recent parallel coloring algorithm for the shared memory programming model, proposed by Gebremedhin

and Manne, to solve the new coloring problem.

This algorithm is being implemented, and will be applied to solve the Jacobian and Hessian estimation

problems in parallel. Once this is complete, we will extend these ideas to solve the estimation problem on

parallel computers with message-passing programming models.

This is joint work with Assefaw Gebremedhin (University of Bergen, Norway, who is currently visiting

Old Dominion University), and Ferderik Manne (University of Bergen, Norway).

High-order compact simulation of wave propagation in non-uniform 
ows Alex Povitsky

The goal of this study is to gain computational insight into physical mechanisms of angular redistribution

of acoustic energy and acoustic pressure while the sound waves propagate in non-uniform compressible 
ow

in the presence of a stagnation point. The idealized mean 
ows mimic real-world 
ows in areas of strong

sound refraction such as a leading edge of a wing or a turbine blade, a protruding corner of a wall cavity, a

wing-fuselage intersection, an impingement area of a jet, and an area behind a blu body. In terms of acoustic energy, the modied sound directivity in the presence of stagnation 
ow is mainly

caused by redistribution of potential and kinetic components of acoustic energy (while sound propagates

upstream) and by angular redistribution of acoustic energy (while directions of the mean 
ow and sound

propagation are far from collinear). Taking into account the compressibility of the background 
ow, (i.e.,

non-uniform distribution of density and speed of sound) the maximum of acoustic pressure moderately

increases (within 6%) while local Mach number M  0:6: The pump of acoustic energy from the background


ow by means of baroclinically generated vorticity is minor. The propagation of acoustic pulse upstream

of the 
ow around the 2D circular cylinder is modeled. The time-averaged root mean square of acoustic

pressure (rms) is presented as a function of angle from the centerline. To compare with the static ambient

conditions, the rms of acoustic pressure at the centerline is about 40% increased for the mean velocity with

M1 = 0:4: The same degree of amplication of sound remains for the 60osector on either side from the

centerline.

In collaboration with Jan Hesthaven (Brown University), we apply his unstructured high-order code to

simulate amplication of sound around more complex 2D and 3D shapes.

17
Tra jectory-based approach to CFD optimization of HiPco reactor for production of carbon

nanotubes

Alex Povitsky and Manny Salas

This study was motivated by an attempt to optimize the High Pressure carbon oxide (HiPco) process

for the production of carbon nanotubes from gaseous carbon oxide. The goal is to achieve rapid and

uniform heating of catalyst particles by an optimal arrangement of jets. Single- and multi-wall nanotubes

are interesting nanoscale materials for aerospace applications for three reasons: A single-wall nanotube can

be either metallic or semiconducting, depending on how exactly the hexagons forming the sheet line up.

In addition, it is also possible to connect two nanotubes with dierent electrical properties. Quasi onedimensional hetero junctions, including metal-metal and metal-semiconductor, can thus be created, resulting

in nanoscale electronic components. These nanotube hetero junctions with electronic switching properties

can be used for developing next-generation of computer components. Single- and multi-wall nanotubes have very good elastomechanical properties, thus they have great potential for spacecraft components requiring

lightweight, highly elastic, and very strong brous material.

Jet mixing in a reactor for production of carbon nanotubes from gaseous carbon oxide initiated by

catalyst particles is studied numerically using a mixed Eulerian and Lagrangian approach. To achieve rapid

monotonic heating of catalyst particles, the behavior of particle tra jectories is studied. Three types of

tra jectories are observed. The particle tra jectories can be bent either towards the interior of the cold jet

(type 1), or outward (type 2). They also can rotate in the vortical zone upstream of the intersection of cold

and hot jets (type 3). Direct exposure to the action of hot jets leads to the rst or to the third type of

tra jectory behavior that causes slow or oscillating heating, respectively. Straightforward measures such as

increasing hot gas consumption, increasing the angle between hot and cold incident jets, and splitting the

cold jet are not sucient to achieve fast heating because of the behavior of particle tra jectories. A modied

reactor design has been proposed, Design C, which includes three parallel nozzles for cold central jets. To

avoid direct exposure of tra jectories to the action of hot jets, the cold jet nozzles are located between the

hot peripheral jet nozzles. Type 1 tra jectories are avoided and at the optimal angle between jets,  = 60o; the heating rate reaches 3:5o  4:5o 105K=sec; a signicant improvement compared to the rate achieved

by the basic design.

This research is in the center of interdisciplinary collaboration between 
uid modeling (ICASE, M. Salas

and A. Povitsky), kinetic modeling (group at NASA Ames), simulation of nanotube growth (group at NASA

Johnson), and physical experiments (group of Professor Smalley at Rice University). Kinetic modeling and

simulation of nanotube growth require a tremendous amount of computer resources. Parallel and distributed

computing, data-parallel, and task-parallel ways to exploit supercomputers will be considered in our future

research.

Numerical modeling of high-incidence three-dimensional lid-driven cavity 
ow

Alex Povitsky

This research studies truly three-dimensional impinging 
ows in a spatial corner with high angle of

incidence between the 
ow and surrounding rigid walls. To keep the simple cubic geometry, the threedimensional rectangular cavity 
ow is considered where the cavity lid moves along its diagonal. The liddriven cavity 
ow mimics many aeronautical, environmental, and industrial 
ows. The secondary 
ow and

the strength of secondary vortices are substantially larger than those in the previous studies where the lid

moves along its edge. If the lid moves along its edge (the classical CFD test case), the 
ow is parallel to the

18
side walls and separation occurs due to the pressure gradient caused by its impingement into the front wall.

In real life a 
ow is likely to be non-parallel to the cavity edges. The non-zero angle of incidence between

the 
ow and a side wall leads to enhanced 
ow separation in comparison with the previous studies.

The three-dimensional lid-driven cavity 
ows are studied by numerical modeling using second-order

upwind schemes for convective terms. This study shows that in spite of the lower level of the primary 
ow

velocity (in the direction of moving lid), the numerous secondary vortices (in the perpendicular direction)

are stronger than those in the classical case. Transition to the unsteady non-symmetric 
ow occurs for

considerably smaller Re numbers.

While the steady-state solution and some transient features are predictable using second-order schemes,

the detailed study of generation of unsteady Gortler vortices (i.e., lose of stability and transition to turbulence) is possible only by use of higher-order compact schemes. Our future research includes parallelization of

compact schemes for incompressible elliptic solvers and use of parallel computers for simulation of transient

process.

Parallel solution techniques for radiation transport equations

Linda Stals

One area of focus in the current ASCI initiative is the solution of radiation transport equations. The

solution of such equations is challenging as they contain strong non-linearities and large jumps in the coe-

cients. We are interested in implementing ecient algorithms that will allow us to solve these problems on

parallel machines containing a large number of processors.

We have investigated two dierent components of the solution of radiation transport equations; we have

compared the parallel performance of two nonlinear solvers, and studied the use of adaptive renement to

better capture the shape of the radiation wave front as it moves through the domain. We have shown that

on up to 16 processors the two nonlinear solvers are competitive with one another. These experiments need

to be rerun on bigger machines to determine if this trend continues when more processors are used. The use

of adaptive renement has proved to be benecial in aiding the solution process.

In the current work we make certain assumptions about the physical domain to help simplify the equations. Our goal now is to remove some of these assumptions.

19
FLUID MECHANICS

Laser-induced thermal acoustics (LITA) for 
ow diagnostics

Roger Hart

There is a recognized need for a seedless equivalent of laser doppler velocimetry (LDV) for use in 
ows

where seeding is undesirable, ineective, or impossible. The requirement for `seedless LDV' is a severe one:

what is wanted is not merely a technique that can be demonstrated in the laboratory, but a technique

that can be successfully embodied in rugged, reliable hardware and applied in real-world environments by

people who are not professional optics researchers. Laser-induced thermal acoustics (LITA) has been under

development for several years at Langley and a few other places as a means of meeting this need. Our goal

is to develop LITA to the point where it becomes widely recognized as the seedless alternative to LDV.

The ma jor accomplishment during the current reporting period was the rst test of LITA velocimetry

in a real-world wind tunnel. During the previous reporting period a compact one-
ow-component LITA

velocimeter was constructed and tested in the laboratory. This instrument uses a novel method of quadraturephase heterodyne detection that 1) is much more stable than previous methods, 2) recovers 
ow direction as well as speed, and 3) signicantly improves precision and accuracy for 
ow velocities below 20 m/s. The LITA

velocimeter was employed at the Basic Aerodynamics Research Tunnel (BART) at NASA Langley during

a 40-day test period. Numerous comparisons with a pitot-static probe in the freestream showed agreement

to within 0:5 m/s for velocities in the range 30{55 m/s, and agreement to within 1 m/s for velocities

in the range 0{30 m/s. The 
ow eld behind a rearward-facing step was mapped in detail and showed

all the expected features, such as 
ow separation and reattachment, a shear layer, and recirculation and

secondary separation. Comparison with LDV gave excellent agreement in the freestream, with discrepancies

in turbulent regions attributable to velocity bias in the LDV measurements. Overall, our rst-generation

LITA apparatus proved to be already the near equal of LDV in terms of accuracy, precision, stability, and

ease of use. The potential of LITA as a practical, dependable, routinely usable 
ow diagnostic is evident when

one considers that LDV has been in use for approximately 30 years and is a thoroughly mature technology. An improved, two-
ow-component LITA velocimeter is now under design, which will incorporate the

lessons learned during the BART test. It will feature improved stability and totally remote (hands-o )

operation. We are currently scheduled to return to BART in April 2002 to make measurements in the slat

cove region of a high-lift wing conguration; sometime after that we will make measurements on supersonic


ows around a blunt body at the Probe Calibration Tunnel (PCT) at NASA Langley. This work was conducted in collaboration with R. J. Balla and G. C. Herring (NASA Langley).

Mapping closure approximation to conditional dissipation rate for turbulent scalar mixing

Guowei He

This work is the rst part of our research on a developing probability density function (PDF) method

for turbulence modeling.

A novel mapping closure approximation (MCA) technique is developed to construct a model for the

conditional dissipation rate (CDR) of a scalar in homogeneous turbulence. It is shown that the CDR model

from amplitude mapping closure is incorrect in asymptotic behavior for unsymmetric binary mixing. The

correct asymptotic behavior can be described by the CDR model formulated by the MCA technique. The

MCA approach is outlined for constructing successive approximation to probability density function and

conditional moment.

20
We will further develop the general principles for mapping closure approximation.

This research was conducted in collaboration with R. Rubinstein (NASA Langley).

Eects of eddy viscosity on time correlations in large eddy simulation

Guowei He

We have established a database for isotropic homogeneous turbulence. The next goal is to calibrate and

develop subgrid models for turbulent 
ows.

Subgrid-scale (SGS) models for large eddy simulation (LES) have generally been evaluated by their

ability to predict single-time statistics of turbulent 
ows such as kinetic energy and Reynolds stresses.

Recent applications of large eddy simulation to the evaluation of sound sources in turbulent 
ows, a problem

in which time correlations determine the frequency distribution of acoustic radiation, suggest that subgrid

models should also be evaluated by their ability to predict time correlations in turbulent 
ows.

This work compares the two-point, two-time Eulerian velocity correlation evaluated from direct numerical

simulation (DNS) with that evaluated from LES, using a spectral eddy viscosity, for isotropic homogeneous

turbulence. It is found that the LES elds are too coherent, in the sense that their time correlations decay

more slowly than the corresponding time correlations in the DNS elds. This observation is conrmed by

theoretical estimates of time correlations using the Taylor expansion technique. The reason for the slower

decay is that the eddy viscosity does not include the random backscatter, which decorrelates 
uid motion at

large scales. An eective eddy viscosity associated with time correlations is formulated, to which the eddy

viscosity associated with energy transfer is a leading-order approximation.

This work is a collaborative eort with L.-P. Wang and R. Rubinstein (NASA Langley).

Lattice Boltzmann equation on a two-dimensional rectangular grid

Li-Shi Luo

The method of the lattice Boltzmann equation (LBE) is usually associated with uniform and symmetric

meshes, such as triangular and square ones in two dimensions and a cubic one in three dimensions. This

feature is due to the symmetry imposed by the discretization in the (particle) velocity space. This limits

the application of the LBE method to situations in which highly asymmetric meshes are needed (such as

stretched meshes with very high aspect ratio in the boundary layer). The present work proposes an LBE

scheme on a rectangular grid.

We propose a generalized LBE nine-velocity model in two-dimensional space with rectangular grids. The

model is based upon the previously proposed generalized LBE nine-velocity model on a square lattice that

is constructed in moment space instead of velocity space, and possesses a maximum number of adjustable

parameters allowed by the freedom of the LBE model. We analyzed the model and found that, in order to

attain the isotropy of model, the sound speed has to be adjusted according to the grid aspect ratio. We also numerically tested the model for three cases: (a) a vortex moving with a constant velocity on a mesh with

periodic boundary conditions; (b) Poiseuille 
ow with an arbitrary inclined angle with respect to the lattice

orientation; and (c) a cylinder asymmetrically placed in a channel. The numerical results of these tests are

compared with either analytic solutions or the results obtained by other methods.

A paper entitled \Lattice Boltzmann Equation on a Two-dimensional Rectangular Grid," authored by

M'hamed Bouzidi, Dominique d'Humieres, Pierre Lallemand, and Li-Shi Luo, has been accepted by the

Journal of Computational Physics (2000). An ICASE report is under preparation.

The present work is a result of collaboration with Pierre Lallemand (Laboratoire ASCI-CNRS, Universite

Paris-Sud (Paris XI Orsay), France), and Dominique d'Humieres (Ecole Normale Superieure, Paris, France).

21
The present work has been partially funded by NASA Langley Research Center under the program of

\Innovative Algorithms for Aerospace Engineering Analysis and Optimization."

We intend to extend our work to 3D LBE models or other more complicated LBE models with larger number of velocities.

Vibrationally induced instabilities in thermocapillary and binary 
uid systems

J. Raymond Skarda

G-jitter is a potential source of instability in 
uid systems on space based platforms. The impact of

residual accelerations (g-jitter) on materials processing applications involving thermocapillary and binary


uid systems are of particular interest. This work consists of two tasks: the rst is to complete analysis of

and nalize reporting of a study concerning gravity modulation of a 
uid layer with surface tension along

its free surface. The second task is to examine bursting behavior that occurs in a binary 
uid system, and

the sensitivity of this behavior to g-Jitter.

Floquet theory was successfully applied to compute stability boundaries of the gravity modulated

Marangoni problems. Fundamental dierences in the behavior of the stability boundaries were observed

with respect to the purely buoyancy (modulated Rayleigh-Benard) problems. Simple stability criteria were

obtained from reduced (one-term Galerkin) formulations of the problem. Final revisions of the paper entitled:

\Instability of a Gravity Modulated Fluid Layer with Surface Tension Variation," were completed, and the

paper is to appear in the Journal of Fluid Mechanics, Vol 434. Preliminary simulations of the binary 
uid

system have been performed using a solver written by Dr. David Jacqmin. Empirical eigenfunctions have

successfully been computed using programs written by Skarda. A reduced-order model has been developed,

however, preliminary results are in poor agreement with results obtained directly from the Jacqmin code.

The disagreement of the lower order model results with direct numerical simulation will be examined.

Eects of vibration (in the context of gravity modulation) imposed on the binary 
uid system will then be

examined using both computational and reduced-order models.

22
STRUCTURES AND MATERIALS

Closed-shell carbon nanostructures from organo-metallic precursors

Theo Dingemans

Single-wall and multi-wall carbon nanotubes are heralded as a new generation of materials with many

high-end applications in electronics, composites, and the medical eld. To date, not many of these ideas

have materialized and not much progress is expected until some key problems are resolved. One of the problems is the production and processability of carbon nanostructures. Practically, all carbon nanostructures

production facilities rely on high temperature laser ablation techniques or high-pressure carbon monoxide

techniques (HiPCO). The last method has been reasonably successful with respect to producing single-wall

carbon nanotubes (SWNTs) in acceptable quantities. Nevertheless, purication with strong oxidizing agents

is often necessary to remove amorphous carbon, catalyst, and other undesirable side products. Purication

of nanotubes produced via HiPCO can result in a yield as low as 50% of acceptable, but not necessarily

superior quality nanotubes. The solubility of nanotubes is another ma jor point of concern. Most industries depend on solution-based processing techniques that will enable them to transport starting materials,

intermediates, and products, and perform chemical transformations followed by dissolving, extracting, etc.

Presently, carbon nanotubes are available in dry form (\bucky paper") or as meta-stable colloidal suspensions in toluene or other solvents. Regardless of the form in which the nanotubes are available, it remains

virtually impossible to take full advantage of their unique properties because they are insoluble and very

resistant towards common chemistries. Currently, we are investigating the use of organo-metallic precursors

towards the synthesis of closed-shell carbon nanostructures.

As a starting point we have synthesized and characterized three isomeric phenyl-alkyne cobalt complexes.

All compounds are soluble and have a high C-H ratio. The dierent substitution patterns (regio-isomers)

will give us information about how substitution patterns aect the formation of pre-graphitic networks.

Although some of the synthetic steps were challenging, we have optimized the synthetic routes and we are

now able to provide multigram quantities of these organo-metallic precursors.

Future work will include processing the precursor molecules using conventional spin casting and vapor

deposition techniques. We envision that this approach will allow us to fabricate ceramic, polymer, and

bio-based sensors and devices from in-situ formed carbon nanostructures. In addition, we will explore the

possibility of incorporating hetero atoms such as nitrogen (N) and Boron (B) and investigate their electronic

properties in applications such as one-dimensional semiconductors and eld eect transistors (FETs).

This research was conducted in collaboration with Mia Siochi (NASA Langley).

Constitutive modeling of nanostructured materials

Vasyl Michael Harik

Nanostructured materials and carbon nanotubes, in particular, appear to possess extraordinary physical properties (e.g., high stiness-to-weight and strength-to-weight ratios and large electrical and thermal

conductivities). Potential applications of these materials range from new electronic devices and electromechanical probes to multifunctional structural components and control systems for aerospace industries. The

goal of this research is to develop constitutive models for advanced material systems involving various nanostructures.

To examine the validity and possible limitations of the continuum models for carbon nanotubes, the

mechanical behavior of a nanotube under axial compressive loads is investigated. The underlying assumptions

23
of continuum models are analyzed along with the governing equations and macromechanical concepts used

in the models. Non-dimensional analysis of the buckling behavior and geometric and material parameters is

carried out. The values of critical strains for various nanotubes are derived and compared with molecular

dynamics simulations. Model applicability maps are constructed for dierent nanotube geometries in the

parameter space.

Future research involves analysis of the nanotube-based AFM tips and other scanning probes along with

further development of modeling capabilities for the constitutive behavior of nanostructured materials.

This research is conducted in collaboration with T. Gates and M. Nemeth (NASA Langley) as well as

other scientists and engineers under the guidance of D. Ambur (NASA Langley).

Constitutive modeling of electromechanical eects in multifunctional materials

Vasyl Michael Harik

Design of new aerospace structures, such as 
exible wings, structures with active controls, multifunctional

membranes, and in
atable electromagnetic antennas require fundamental understanding of electromagneticthermoelastic material behavior so that they can be modeled accurately in structural analyses. The ob jective

of this research is to develop constitutive models for multifunctional materials.

A class of nanostructured piezoelectric polymers is considered in order to identify the key physical

phenomena contributing to the mechanical and electrical properties of multifunctional polymer lms. The

physical and materials science characterization of the key material parameters has been analyzed prior to

deriving functional relations. The form of functional relations depends on the feedback from the dimensional

analysis and electromechanical models that are examined for such material systems. The work performed thus

far indicates that the dimensional analysis of material behavior may lead to characteristic non-dimensional

parameters that would control material constitutive response.

Future work involves derivation of the general and explicit functional relations between material parameters as well as validation of such relations by experimental data.

This research is conducted in collaboration with D. Ambur (NASA Langley) and Z. Ounaies (ICASE).

Progressive failure analysis of composite materials

Vasyl Michael Harik

In-service failures of complex material systems are generally dicult to predict. In aerospace applications, the use of composite structures permits optimization of their design not only for weight and mechanical

performance but also for a predictable failure pattern. In laminated structures, damage accumulation processes have progressive character which depends on the material properties, the ply-stacking conguration,

and the type of loading. The goal of this research is to assess the failure criteria and damage models for

advanced composite systems considered in the NASA White Paper on Progressive Failure Analysis.

The current assessment of basic concepts, mathematical and physical models of composite behavior

is based on the previous reviews and some recent studies such as an International Exercise on Failure of

Composites organized by DERA (UK) and the Low Cycle Fatigue Program of the U.S. Army Research

Laboratory (Aberdeen, MD). The analysis of micromechanical and hierarchical modeling stems from the work carried out in cooperation with the Sandia National Laboratories (Albuquerque, NM). The rst phase

contribution to the NASA White Paper has been completed.

This work will be further developed by other NASA researchers.

24
This research is conducted under the guidance of D. Ambur (NASA Langley) and in collaboration with

C. Davila (NASA Langley) and other NASA engineers.

Progressive failures studies of composite panels with and without cutout

Navin Jaunky

The use of composite materials for aircraft primary structures can result in signicant benets on aircraft

structural cost and performance compared to conventional metallic structures. However, unlike conventional

metallic materials, composite structures fail under dierent failure modes such as matrix cracking, bermatrix shear failure, ber failure, and delamination. The initiation of damage in a composite laminate

occurs when a single ply or part of the ply in the laminate fails in any of these failure modes over a certain

area of the structure. The initiation of damage does not mean that the structure cannot carry any additional

load. The residual load-bearing capability of the composite structure from the onset of material failure or

initiation of damage to nal failure can be quite signicant. It is at the nal failure load that the structure

cannot carry any further load.

Accurate determination of failure modes and their progression helps either to devise structural features

for damage containment or to dene fail-safe criteria. Therefore, it is important to understand the damage

progression in composite structures sub jected to dierent loading conditions. Hence the ob jective of the

present study is to develop and validate an ecient methodology that can predict the ultimate strength of

composite panels by taking into account ply damage modes and geometrical nonlinear response. Geometric

nonlinear response is important since aircraft structures are thin-wall structures and undergo signicant

deformation.

The nite element implementation of this progressive failure analysis was developed for the ABAQUS

structural analysis program using the USDFLD user-written subroutine. ABAQUS calls this USDFLD

subroutine at all material points of elements that have material properties dened in terms of the eld

variables. The eld variables represent the material damage modes and in this study the damage modes

considered are those dened by Hashin criteria. When a damage mode has been detected, the mechanical

properties in the damaged area are degraded appropriately, according to the Chang degradation model, which

is a ply discount model. Delamination failure mode is not included in the present study. The subroutine

provides access points to a number of variables such as stresses, strains, material orientation, current load

step, and material name, all of which can be used to compute the eld variables. Stresses and strains are

computed at each incremental load step and evaluated by the failure criteria to determine the occurrence

and the mode of failure.

Progressive failure analyses were carried out for 
at panels and curved panels with and without cutout.

The 
at panels were sub jected to shear loading, while the curved panel was sub jected to compression.

A bead-stiened panel sub jected to shear loading was also considered. These test cases were considered

since data from NASA-conducted experiments was available. Results from progressive failure analyses are

in good agreement with experimental results when delamination is not the ma jor damage mode. In some

cases, including measured geometric imperfection in the nite element model provides better agreement with

experiment results.

Future work will focus on more comparisons of progressive failure analyses with experiments that have

recently been carried out.

This work was done in collaboration with Damodar R. Ambur, Carlos G. Davila, and Mark W. Hilburger

(NASA Langley).

25
Debonding in stringer reinforced composite components

Ronald Krueger

Many composite components in aerospace structures are made of 
at or curved panels with co-cured

or adhesively bonded frames and stieners. Testing of stiened panels designed for pressurized aircraft

fuselage has shown that bond failure at the tip of the frame 
ange is an important and very likely failure

mode. Comparatively, simple specimens consisting of a stringer 
ange bonded onto a skin were developed

in previous investigations. The failure that initiates at the tip of the 
ange in these specimens is identical

to the failure observed in the full-scale panels and the frame pull-o specimens. The ob jective of this work

is to investigate the damage mechanisms in composite bonded skin/stringer constructions and to develop a

methodology for cumulative life using delamination fatigue characterization data and geometric nonlinear

nite element analysis.

The damage mechanisms in bonded composite skin/stringer structures under tension fatigue loading

conditions was studied. Microscopic investigations of the specimen edges were used to identify typical

damage patterns and to document the onset of matrix cracking and delamination as a function of fatigue

cycles. Subsequently, an analytical methodology to accurately predict the onset of matrix cracking as well as delamination was demonstrated. The tension loading was simulated in a geometrically nonlinear

plane-stress nite element model using the ABAQUS
r FE code. A stress analysis was used to predict

the location and orientation of the rst transverse crack based on the principal transverse tension stress

distribution in the 
ange tip area. Computed stresses for dierent load levels were compared to material

characterization data from transverse tensile fatigue tests to generate a curve predicting the onset of matrix

cracking. A fracture mechanics approach was used to determine delamination growth from this transverse

crack. Delaminations of various lengths were discretely modeled by releasing multipoint constraints at the

locations where delaminations were observed during the experiments. Mode I and II strain energy release

rate contributions, GI and GII, were calculated for all load cases using the virtual crack closure technique.

Computed peak G values were used with G versus N fatigue characterization data to predict the fatigue life

of the skin/stringer specimens. A cumulative life prediction methodology was developed by combining the

results for fatigue life for matrix crack onset and fatigue life for delamination onset.

The current studies were used to identify failure curves for the onset of the rst failure in a virgin,

as-designed, conguration.

Future work will focus on analyses to compare current results with (a) simulated rst failure by delamination from an assumed matrix crack, (b) simulated rst failure from an assumed delamination in the bond

line, and (c) simulated delamination in the skin with no matrix crack present. This comparison may then

also be extended to a more classical damage tolerance approach assuming delamination from a \critical size"

initial 
aw at the most \critical location."

This work was done in collaboration with Isabelle L. Paris (National Research Council), T. Kevin

O'Brien (Army Research Laboratory, Vehicle Technology Directorate located at NASA Langley), and Pierre

J. Minguet (The Boeing Company).

The in
uence of crosslinks on physical aging in glassy thermoplastic polyimides

Lee M. Nicholson

Durability and long-term performance are among the primary concerns for the use of advanced polymer

matrix composites (PMCs) in modern aerospace structural applications. For a PMC sub jected to long-term

exposure at elevated temperatures, the viscoelastic nature of the polymer matrix will contribute to macro26
scopic changes in composite stiness, strength, and fatigue life. Over time, changes in the polymer due to

physical aging will have profound eects on the viscoelastic compliance of the material, hence aecting its

long-term durability. This research aims to investigate the use of polymer viscoelasticity at the microstructural level to accurately predict how changes in chemical structure, physical structure, and state of stress in

the polymer impact the mechanical properties of advanced polymers.

Experiments were performed using ve variations in crosslink density to evaluate the dierences in mechanical performance of an advanced polyimide. The physical aging behavior was isolated by conducting

sequenced, short-term isothermal creep compliance tests in tension. These tests were performed over a range

of sub-glass transition temperatures. The material constants, material master curves and physical agingrelated parameters were evaluated as a function of temperature and crosslink density using time-temperature

and time-aging superposition techniques. The time-temperature superposition analysis of the creep compliance showed that high crosslink density materials have increased creep compliance and increased creep

rate, and are less sensitive to physical aging compared to low crosslink density materials. The temperature

sensitivity of the time-temperature superposition (TTSP) shift factor was shown to increase monotonically

with increasing crosslink density. This research has signicant implications for the composites and resins

community since it's a widely accepted practice to use crosslinks to provide thermal and mechanical stability. This research has shown that the introduction of crosslinks signicantly interferes with the mechanisms of

physical aging making the glassy resin behave dierently than expected.

The eects of creep loading for long timescales (> 1100 hours) will provide a means for evaluating

a predictive model, and the long-term eects of crosslink density and temperature. The initial model

predictions compare favorably with the long-term test data. This work is continuing to develop constitutive

relationships to express the long-term mechanical performance of the material.

This research is done in collaboration with Thomas S. Gates, Karen S. Whitley and Jerey A. Hinkley

(NASA Langley).

High-temperature piezoelectric lms

Zoubeida Ounaies

Developing high-performance, high-temperature 
exible piezoelectric materials for active 
ow control

sensors and airframe health monitoring sensors is a critical component of NASA's Morphing Program, which

is focused on investigating smart and biomimetic material applications that will enable self-adaptive 
ight

with improved performance and safety in next generation aircraft and spacecraft. One such application is the

design and development of high-performance, high-temperature, 
exible piezoelectric polymers. This application was the impetus for a study in which NASA LaRC has synthesized a series of polyimides containing

polar functional groups. Additionally, the resultant piezoelectric response was assessed and a fundamental

structure-property analysis was performed. Eects of structural changes, including variations in the type

and concentration of dipolar groups, on the piezoelectric behavior is examined. The remanent polarization,

the dielectric relaxation strength, and the various piezoelectric coecients were measured. Polymers with multiple nitril groups showed out-of-plane displacement that exceeded that of state-of-the-art PVDF. Large

directionality in the piezoelectric behavior was seen where the in-plane coecients were more than one order of magnitude smaller than the out-of-plane values. The thermal stability of the piezoelectric eect was

evaluated under dynamic and static thermal stimuli. These materials exhibited good thermal stability of

the piezoelectric properties up to 100C. This work was presented at the American Chemical Society Poly

Millennial 2000, December 10, 2000 (Waikoloa, Hawaii). The polymers show very promising behavior for

27
use as high-temperature sensors, and they possess distinct improvements over state-of-the-art piezoelectric

lm sensors including enhanced polarization, polarization stability at elevated temperatures, and improved

processability. Future work will further explore the processing and properties of the polyimide/PZT composites. This work is done in collaboration with Joycelyn S. Harrison (NASA Langley), Cheol Park (ICASE), and Dan

Klein (NRC).

Piezoelectric ceramics for use as actuators

Zoubeida Ounaies

Implementing piezoelectric actuators in vibration and noise suppression applications is steered towards

improving spacecraft and aircraft operation. This may lead to reduction of control electronics size and cost,

and a lowering of the voltage drive by using thinner, more ecient, and better characterized actuators.

THUNDER (THin UNimorph DrivER) actuators are pre-stressed piezoelectric devices developed at NASA

LaRC that exhibit enhanced strain capabilities. As a result, they are of interest in a variety of aerospace and

aircraft applications. Their performance as a function of electric eld, temperature, and frequency is needed

in order to optimize their operation. Towards that end, a number of THUNDER devices were obtained from

FACE Co. with stainless steel thicknesses varying from 1 mil to 20 mils. The various devices are evaluated

to determine low-eld and high-eld displacement as well as the polarization hysteresis loops as a function

of frequency. The thermal stability of these drivers was evaluated by two dierent methods. First, the

samples were thermally cycled under electric eld by systematically increasing the maximum temperature

from 25C to 200C while the displacement was being measured. Second, the samples were isothermally

aged at an elevated temperature in air, and the isothermal decay of the displacement was measured at room

temperature as a function of time. Results of this study were presented at the SPIE Smart Structures

and Materials Conference, March 4{9, 2001 (Newport Beach, CA). The internal stresses present within the

ceramic and metal layers, combined with restricted lateral motion, enhanced the axial displacement and

caused large asymmetry in the domain switching at high elds. Asymmetry of the hysteresis is most likely

due to stress domains facilitating switching and alignment with positive elds and impeding alignment with

negative elds. To quantify the exact relationship between the state of stress in the ceramic and the overall

performance, we are pursuing modeling of these devices, incorporating both thermoelastic relations and

ferroeletric domain theory. We also plan on continuing the modeling of the nonlinear hysteresis behavior of

piezoelectric ceramics as a function of frequency and temperature.

This work is done in collaboration with Ralph Smith (North Carolina State University and ICASE) and

Karla Mossi (Virginia Commonwealth University and ICASE).

Molecular dynamics simulations of metallic nano-clusters

Sun Mok Paik

For the last decade the nano-sized metallic particles have attracted a lot of attention among scientists

and engineers because of its potential application in a variety of elds, such as improving fracture toughness

of a material, quantum devices, micro-mechanics, etc. The Molecular Dynamics (MD) simulation technique

is an exact (within numerical accuracy of the computer) deterministic numerical simulation method, and

one of the best-suited methods to study local structures of a system. In this investigation, we study the

thermodynamic properties of the nano-sized Au clusters using the Molecular Dynamics simulation.

Using the MD technique we simulate a stable structure of Au clusters sized between ve nanometers

and 30 nanometers on the (001) surface at room temperature T=300K. A many-body Embedded Atomic

28
Method (EAM) potential is used for the interatomic interactions between the gold atoms. We then increase

temperature to T=1300K and monitor structural phase transformation as a function of temperature both

on in-plane and interlayer structures. We nd that the large (> 10 nm) clusters are slightly o-aligned to

underlying substrate (\rotated domain") with rotation angle about 1 whereas the smaller clusters (< 10

nm) are aligned to the substrate (\un-rotated domain"). The rotated domain undergoes a phase transition

to an un-rotated domain at a temperature about 3=4 of the melting temperature. Unlike the bulk materials,

the interlayer distance between the cluster and substrate layer decreases as the temperature increases.

In the future, we will simulate and calculate various mechanical and electric properties of other metallic

nano-particles. We also plan to write a MD code for a parallel computer.

This work was done in collaboration with Min Namkung and R. A. Wincheski (NASA Langley).

A theoretical modeling of quantum transport in carbon nanotube-based magnetic tunnel junctions

Sun Mok Paik

Molecular electronics has taken a large step forward since the discovery of carbon nanotube metallic

and semiconducting molecular wire. Because of the unique structure and electrical properties, the potential

application of these devices are enormous, such as quantum dot, quantum wire, quantum computers, logic

gates, as well as other nano-mechanical devices. The nanotube behaves as ballistic quantum conductors with

long phase-coherence lengths for charge carriers and, thus, it may well be an ideal candidate for achieving

molecular scale magneto-electronics in which both the charge and spin degree of freedom are utilized for the

operation of a functional device. More detailed theoretical modeling and suggestions are needed.

In this pro ject we use the tight-binding Hamiltonian model,

H = Vpp X

<y>

a+

i aj ;

to calculate the energy band of a carbon nanotube where Vpp = 2:75 for a single-wall carbon nanotube, and

ay and a are the creation and destruction operators. Using this Hamiltonian, the Green's function of the

carbon nanotube base magnetic tunnel junction that consists of a Single-wall Carbon NanoTubes (SWNT)

connected to two ferromagnetic (FM) electrodes is calculated,

Gr(a)(E) = 1

E  Htube  Pr(a)

L Pr(a)R

;

where r=a stands for retarded/advanced. Pr(a)

L and Pr(a)R are the retarded Green's function for the left

and right electrodes, respectively. The magnetic moments of two FMs are pointing dierent directions so

that we can investigate the spin-dependent quantum transport properties. The density of the state (DOS)

and the conductivity of the system are calculated from the Green's function. We nd that the resistance

between two FM electrodes is minimal ( 6:4k
 for armchair tube with the length obeyed by 3n + 1 rule)

when the magnetic moments of two electrodes are parallel, and maximum when the magnetic moments are

anti-parallel. The change in the resistance is about 20%. These results will be compared and used in an

ongoing experimental pro ject in the Nondestructive Evaluation Science Branch of NASA Langley. In the future, we will use MD simulation techniques to nd more realistic interface structure between

electrode and carbon nanotube. This result will be used to more quantitative prediction for the quantum

transport properties in carbon nanotube-based tunnel junctions.

This work was done in collaboration with Min Namkung and R. A. Wincheski (NASA Langley).

29
Corona poling of partially cured polyimide

Cheol Park

A series of amorphous piezoelectric polyimides containing polar functional groups has been developed at

NASA LaRC for potential use as high-temperature sensors and actuators in aircraft and aerospace applications. They exhibited a piezoelectric response at temperatures in excess of 150C and good thermal stability. The level of piezoelectricity in the amorphous polyimides, however, is an order of magnitude lower than what

is required for practical utility in devices. In an attempt to maximize the degree of dipolar orientation and

the piezoelectric response, a new poling method was introduced and evaluated.

In-situ poling and imidization of partially cured polyimides was studied to achieve the required piezoelectricity. A positive corona poling was used to minimize localized arcing during poling and allow additional variations in the poling process. The dielectric relaxation strength, remanent polarization, and piezoelectric

responses were evaluated as a function of the poling prole. The partially cured, corona-poled polymers

exhibited higher dielectric relaxation strength ("), remanent polarization (Pr ), and piezoelectric strain coecient (dt) than a fully cured, conventionally poled one. A response comparable to that of the piezoelectric

polymer PVDF was attained from the amorphous polyimides with higher thermal stability. This study was

presented at the American Chemical Society Biennial Meeting in Hawaii, December 2001.

Future research will be focused on assessing the stability of the piezoelectricity of the partially cured

corona-poled polymers. Application of the in-situ poling and imidization of partially cured polyimides for

amorphous polyimides containing higher dipolar concentration will be investigated.

This research was performed in collaboration with Zoubeida Ounaies (ICASE), Kris Wise (NRC), and

Joycelyn Harrison (NASA Langley).

Single-wall carbon nanotube polymer composites

Cheol Park

Carbon nanotubes are of great interest because of their unique electronic and mechanical properties

combined with their chemical stability. In this study, single-wall carbon nanotube (SWNT) polymer composites were prepared and characterized as part of an eort to develop polymeric materials with improved

combinations of properties for potential use as thin lms on future spacecraft. Next generation spacecraft

will require ultra-lightweight materials that possess specic and unique combinations of properties such as

radiation and atomic oxygen resistance, low solar absorptivity, high thermal emissitivity, electrical conductivity, tear resistance, ability to be folded and seamed, and good mechanical properties. The ob jective of

this work was to incorporate sucient electrical conductivity into space-durable polymers to mitigate static

charge build-up. The challenge is to obtain this level of conductivity (106  108 S/cm) without degrading

other properties.

Several dierent approaches were attempted to fully disperse the SWNTs into the polymer matrix.

These include high shear mixing, sonication, and synthesizing the polymers in the presence of pre-dispersed

SWNTs. The eect of SWNT concentration and dispersion of the nanocomposites on the conductivity, solar absorptivity, and mechanical properties were investigated. The SWNT/polyimide nanocomposite lms

exhibited signicant increases in surface and volume conductivity at relatively low loading (< 0:2wt%)

levels with some loss of optical transmission and increase in color (solar absorptivity). Tensile properties

and thermal stability were noticeably improved at 1wt% SWNT. The dispersion of SWTNs was evaluated

with optical, transmission electron, and scanning probe microscopes. This study was presented at the

Nanospace 2001 conference in Galveston, TX on March 2001.

30
Investigation of alternative methods of dispersing SWNTs in polymer matrices are continued. Chemical modication of a SWNT surface to aid in dispersion will also be studied. Electrospinning of the

SWNT/polymer solution will be studied to develop engineering nanobers for potential use as sensors and

actuators in aerospace applications.

This research was performed in collaboration with Zoubeida Ounaies (ICASE), Kent Watson (NRC),

Joycelyn Harrison (NASA Langley), and John Connell (NASA Langley).

Organic-inorganic hybrid-clay nanocomposites

Cheol Park

Polymer-clay nanocomposites are of great interest for many industrial applications due to their light weight, high strength, modulus, and toughness, tear/rip resistance, radiation resistance, low coecient of

thermal expansion, low permeability of atoms, low solar absorption, and optical transparency. Layered

silicates (e.g., clay) can provide ecient reinforcement as an inclusion with unique physical and chemical

properties at low loading levels (1{5%) because of their high surface area and aspect ratio if the layered

silicates are completely exfoliated in a host polymer matrix. However, uniform dispersion of completely

exfoliated layered silicates in a polymer matrix has been a dicult task to accomplish. One of the reasons is

lack of compatibility between the hydrophilic clay surfaces and organophilic polymer matrix. To overcome

this thermodynamic barrier, organically modied layered silicates have often been used to intercalate and

exfoliate the layered silicates in a polymer matrix. Complete dispersion of the clays as a single silicate layer

in a polymer matrix, however, has rarely been achieved with the present methods due to the intrinsic strong

attraction among the layers with high surface area. Successfully intercalated and swelled layered silicates

often fail to exfoliate during mixing under shear or sonication, and even exfoliated clay layers tend to reform

stacked layers during solvent evaporation or polymerization process. A novel approach should be designed

to achieve complete dispersion of the clay inclusions in a polymer matrix to achieve the required properties.

Accordingly, it is a primary ob jective of this research to provide a unique method to disperse layered silicates

uniformly as a single layer in a host composite matrix by introducing organic-inorganic hybrid as a matrix.

These nanocomposites were prepared by dispersion of nano-sized inclusions such as layered silicates

(smectite-type clay) into an organic-inorganic hybrid matrix homogeneously without 
occulation. The hydrolyzed silanol groups present in the organic and inorganic precursors subsequently reacted with hydroxyl

groups located on the clay layer edges to form hydrogen and/or covalent bonds. This aided in the dispersion of the clay layers more eciently under high shear. Remaining silanol groups reacted to form a

network structure through self-condensation, thus preventing the dispersed exfoliated single clay layers from

collapsing back to a layered structure during polymerization and lm drying and/or curing. The hybrid-clay

nanocomposite exhibited an increase in tensile properties at low loadings. A transmission electron microscope was used to assess the dispersion of the nanoclays in the matrix resin, which revealed that most of the

layered silicates remained exfoliated and the exfoliated clays are distributed uniformly. Further characterization of the hybrid-clay nanocomposites is underway including the permeation and

X-ray analyses. Various organic-inorganic hybrid systems will be investigated for the hybrid-clay composites.

This research was performed in collaboration with Joseph Smith (NASA Langley) and John Connell

(NASA Langley).

31
REPORTS AND ABSTRACTS

Mehrotra, Piyush, and Hans Zima: High performance Fortran for aerospace applications. ICASE Report No.

2000-31, (NASA/CR-2000-210321), January 2, 2001, 27 pages. To appear in Parallel Computing.

This paper focuses on the use of High Performance Fortran (HPF) for important classes of algorithms

employed in aerospace applications. HPF is a set of Fortran extensions designed to provide users with a highlevel interface for programming data parallel scientic applications, while delegating to the compiler/runtime

system the task of generating explicitly parallel message-passing programs. We begin by providing a short

overview of the HPF language. This is followed by a detailed discussion of the ecient use of HPF for

applications involving multiple structured grids such as multiblock and adaptive mesh renement (AMR)

codes as well as unstructured grid codes. We focus on the data structures and computational structures

used in these codes and on the high-level strategies that can be expressed in HPF to optimally exploit the

parallelism in these algorithms.

Bottasso, Carlo L., Stefano Micheletti, and Riccardo Sacco: Discontinuous dual-primal mixed nite elements

for el liptic problems. ICASE Report No. 2000-37, (NASA/CR-2000-210543), October 18, 2000, 22 pages.

To be submitted to Computer Methods in Applied Mechanics and Engineering.

We propose a novel discontinuous mixed nite element formulation for the solution of second-order

elliptic problems. Fully discontinuous piecewise polynomial nite element spaces are used for the trial and

test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce

new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on

the other avoid the need to dene a priori algorithmic 
uxes as in standard discontinuous Galerkin methods.

Static condensation is performed at the element level, leading to a solution procedure based on the sole

interface unknowns.

The resulting family of discontinuous dual-primal mixed nite element methods is presented in the one

and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit

Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and

two dimensions demonstrate the order accuracy of the new method, conrming the results of the analysis.

Xu, Kun: A gas-kinetic BGK scheme for the compressible Navier-Stokes equations. ICASE Report No. 2000-

38, (NASA/CR-2000-210544), October 30, 2000, 37 pages. To be submitted to the International Journal of

Numerical Methods in Fluids.

This paper presents an improved gas-kinetic scheme based on the Bhatnagar-Gross-Krook (BGK) model

for the compressible Navier-Stokes equations. The current method extends the previous gas-kinetic NavierStokes solver developed by Xu and Prendergast by implementing a general nonequilibrium state to represent

the gas distribution function at the beginning of each time step. As a result, the requirement in the previous

scheme, such as the particle collision time being less than the time step for the validity of the BGK NavierStokes solution, is removed. Therefore, the applicable regime of the current method is much enlarged and

the Navier-Stokes solution can be obtained accurately regardless of the ratio between the collision time

and the time step. The gas-kinetic Navier-Stokes solver developed by Chou and Bagano is the limiting

case of the current method, and it is valid only under such a limiting condition. Also, in this paper, the

32
appropriate implementation of boundary condition for the kinetic scheme, dierent kinetic limiting cases,

and the Prandtl number x are presented. The connection among articial dissipative central schemes,

Godunov-type schemes, and the gas-kinetic BGK method is discussed. Many numerical tests are included

to validate the current method.

Chen, Zhikai, Kurt Maly, Piyush Mehrotra, and Mohammad Zubair: Arcade: A web-Java based framework

for distributed computing. ICASE Report No. 2000-39, (NASA/CR-2000-210545), October 23, 2000, 14

pages. Proceedings of WebNet 2000.

Distributed heterogeneous environments are being increasingly used to execute a variety of large size

simulations and computational problems. We are developing Arcade, a web-based environment to design,

execute, monitor, and control distributed applications. These targeted applications consist of independent

heterogeneous modules which can be executed on a distributed heterogeneous environment. In this paper we

describe the overall design of the system and discuss the prototype implementation of the core functionalities

required to support such a framework.

Lockard, David P., Li-Shi Luo, and Bart A. Singer: Evaluation of the lattice-Boltzmann equation solver PowerFLOW for aerodynamic applications. ICASE Report No. 2000-40, (NASA/CR-2000-210550), November

1, 2000, 48 pages.

A careful comparison of the performance of a commercially available Lattice-Boltzmann Equation solver

(PowerFLOW) was made with a conventional, block-structured computational 
uid-dynamics code (CFL3D)

for the 
ow over a two-dimensional NACA-0012 airfoil. The results suggest that the version of PowerFLOW

used in the investigation produced solutions with large errors in the computed 
ow eld; these errors are

attributed to inadequate resolution of the boundary layer for reasons related to grid resolution and primitive

turbulence modeling. The requirement of square grid cells in the PowerFLOW calculations limited the number of points that could be used to span the boundary layer on the wing and still keep the computation size

small enough to t on the available computers. Although not discussed in detail, disappointing results were

also obtained with PowerFLOW for a cavity 
ow and for the 
ow around a generic helicopter conguration.

Dubrulle, B., and Guowei He: Possible statistics of two coupled random elds: Application to passive scalar.

ICASE Report No. 2000-41, (NASA/CR-2000-210553), November 13, 2000, 21 pages. Submitted to the

European Journal of Physics C.

We use the relativity postulate of scale invariance to derive the similarity transformations between

two coupled scale-invariant random elds at dierent scales. We nd the equations leading to the scaling

exponents. This formulation is applied to the case of passive scalars advected i) by a random Gaussian

velocity eld; and ii) by a turbulent velocity eld. In the Gaussian case, we show that the passive scalar

increments follow a log-Levy distribution generalizing Kraichnan's solution and, in an appropriate limit, a

log-normal distribution. In the turbulent case, we show that when the velocity increments follow a logPoisson statistics, the passive scalar increments follow a statistics close to log-Poisson. This result explains

the experimental observations of Ruiz et al. about the temperature increments.

33
Bauchau, Olivier A., Jou-Young Choi, and Carlo L. Bottasso: On the modeling of shel ls in multibody dynamics. ICASE Report No. 2000-42, (NASA/CR-2000-210556), November 13, 2000, 28 pages. Submitted

to Multibody Dynamics Systems.

Energy preserving/decaying schemes are presented for the simulation of the nonlinear multibody systems

involving shell components. The proposed schemes are designed to meet four specic requirements: unconditional nonlinear stability of the scheme, a rigorous treatment of both geometric and material nonlinearities,

exact satisfaction of the constraints, and the presence of high frequency numerical dissipation. The kinematic

nonlinearities associated with arbitrarily large displacements and rotations of shells are treated in a rigorous

manner, and the material nonlinearities can be handled when the constitutive laws stem from the existence

of a strain energy density function. The eciency and robustness of the proposed approach is illustrated

with specic numerical examples that also demonstrate the need for integration schemes possessing high

frequency numerical dissipation.

Bottasso, Carlo L., Olivier A. Bauchau, and Jou-Young Choi: An energy decaying scheme for nonlinear

dynamics of shel ls. ICASE Report No. 2000-43, (NASA/CR-2000-210557), November 13, 2000, 28 pages.

Submitted to Computer Methods in Applied Mechanics and Engineering.

A novel integration scheme for nonlinear dynamics of geometrically exact shells is developed based on

the inextensible director assumption. The new algorithm is designed so as to imply the strict decay of the

system total mechanical energy at each time step, and consequently unconditional stability is achieved in

the nonlinear regime. Furthermore, the scheme features tunable high frequency numerical damping and it

is therefore stiy accurate. The method is tested for a nite element spatial formulation of shells based

on mixed interpolations of strain tensorial components and on a two-parameter representation of director

rotations. The robustness of the scheme is illustrated with the help of numerical examples.

Ditkowski, A., D. Gottlieb, and B.W. Sheldon: Optimization of chemical vapor inltration with simultaneous

powder formation. ICASE Report No. 2000-44, (NASA/CR-2000-210620), November 27, 2000, 21 pages.

Submitted to Advanced Materials.

A key diculty in isothermal, isobaric chemical vapor inltration is the long processing times that are

typically required. With this in mind, it is important to minimize inltration times. This optimization

problem is addressed here, using a relatively simple model for dilute gases. The results provide useful

asymptotic expressions for the minimum time and corresponding conditions. These approximations are

quantitatively accurate for most cases of interest, where relatively uniform inltration is required. They also

provide useful quantitative insight in cases where less uniformity is required. The eects of homogeneous nucleation were also investigated. This does not aect the governing equations for inltration of a porous

body, however, powder formation can restrict the range of permissible inltration conditions. This was

analyzed for the case of carbon inltration from methane.

Ayala-Rincon, Mauricio, and Cesar Mu~noz: Explicit substitutions and al l that. ICASE Report No. 2000-45, (NASA/CR-2000-210621), November 28, 2000, 27 pages. To appear in the Colombian Journal of Computation.

Explicit substitution calculi are extensions of the -calculus where the substitution mechanism is internalized into the theory. This feature makes them suitable for implementation and theoretical study of

34
logic-based tools such as strongly typed programming languages and proof assistant systems. In this paper we explore new developments on two of the most successful styles of explicit substitution calculi: the - and se-calculi.

Cockburn, Bernardo, and Chi-Wang Shu: Runge-Kutta discontinuous Galerkin methods for convectiondominated problems. ICASE Report No. 2000-46, (NASA/CR-2000-210624), December 5, 2000, 80 pages.

Submitted to SIAM Review.

In this paper, we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods

for non-linear convection-dominated problems. These robust and accurate methods have made their way into

the main stream of computational 
uid dynamics and are quickly nding use in a wide variety of applications.

They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly

stable regardless of its accuracy, with a nite element space discretization by discontinuous approximations,

that incorporates the ideas of numerical 
uxes and slope limiters coined during the remarkable development of

the high-resolution nite dierence and nite volume schemes. The resulting RKDG methods are stable, highorder accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary

conditions. We review the theoretical and algorithmic aspects of these methods and show several applications

including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and

Hamilton-Jacobi-like equations.

Cockburn, Bernardo, Mitchell Luskin, Chi-Wang Shu, and Endre Suli: Enhanced accuracy by post-processing

for nite element methods for hyperbolic equations. ICASE Report No. 2000-47, (NASA/CR-2000-210625),

December 14, 2000, 34 pages. Submitted to Mathematics of Computation.

We consider the enhancement of accuracy, by means of a simple post-processing technique, for nite

element approximations to transient hyperbolic equations. The post-processing is a convolution with a

kernel whose support has measure of order one in the case of arbitrary unstructured meshes; if the mesh is

locally translation invariant, the support of the kernel is a cube whose edges are of size of the order of the

mesh size only. For example, when polynomials of degree k are used in the discontinuous Galerkin (DG)

method, and the exact solution is globally smooth, the DG method is of order k + 1=2 in the L2 norm,

whereas the post-processed approximation is of order 2k + 1; if the exact solution is in L2 only, in which case

no order of convergence is available for the DG method, the post-processed approximation converges with

order k + 1=2 in L2 over a subdomain on which the exact solution is smooth. Numerical results displaying

the sharpness of the estimates are presented.

He, Guowei, and R. Rubinstein: Mapping closure approximation to conditional dissipation rate for turbulent

scalar mixing. ICASE Report No. 2000-48, (NASA/CR-2000-210631), December 14, 2000, 12 pages. To be

submitted to Physics of Fluids.

A novel mapping closure approximation (MCA) technique is developed to construct a model for the

conditional dissipation rate (CDR) of a scalar in homogeneous turbulence. It is shown that the CDR model

from amplitude mapping closure is incorrect in asymptotic behavior for unsymmetric binary mixing. The

correct asymptotic behavior can be described by the CDR model formulated by the MCA technique. The

MCA approach is outlined for constructing successive approximation to probability density function (PDF)

and conditional moment.

35
Shi, Jing, Changqing Hu, and Chi-Wang Shu: A technique of treating negative weights in WENO schemes.

ICASE Report No. 2000-49, (NASA/CR-2000-210632), December 27, 2000, 22 pages. Submitted to the

Journal of Computational Physics.

High order accurate weighted essentially non-oscillatory (WENO) schemes have recently been developed

for nite dierence and nite volume methods both in structured and in unstructured meshes. A key idea

in WENO scheme is a linear combination of lower order 
uxes or reconstructions to obtain a higher order

approximation. The combination coecients, also called linear weights, are determined by local geometry of

the mesh and order of accuracy and may become negative. WENO procedures cannot be applied directly to

obtain a stable scheme if negative linear weights are present. Previous strategy for handling this diculty is

by either regrouping of stencils or reducing the order of accuracy to get rid of the negative linear weights. In

this paper we present a simple and eective technique for handling negative linear weights without a need

to get rid of them. Test cases are shown to illustrate the stability and accuracy of this approach.

Rubinstein, Robert, and Meelan Choudhari: Statistical prediction of laminar-turbulent transition. ICASE

Report No. 2000-50, (NASA/CR-2000-210638), January 5, 2001, 39 pages. To be submitted to Physics of

Fluids.

Stochastic versions of stability equations are considered as a means to develop integrated models of

transition and turbulence. Two types of stochastic models are considered: probability density function

evolution equations for stability mode amplitudes, and Langevin models based on representative stability

theories including the resonant triad model and the parabolized stability equations. The rst type of model

can describe the eect of initial phase dierences among disturbance modes on transition location. The

second type of model describes the growth of random disturbances as transition proceeds and provides a

natural framework in which to couple transition and turbulence models. Coupling of parabolized stability

equations with either subgrid stress models or with conventional turbulence models is also discussed as an

alternative route to achieve the goal of integrated turbulence and transition modeling.

Huyse, Luc, and R. Michael Lewis: Aerodynamic shape optimization of two-dimensional airfoils under uncertain operating conditions. ICASE Report No. 2001-1, (NASA/CR-2001-210648), January 16, 2001, 13

pages. To appear in the Proceedings of the International Conference on Structural Safety and Reliability. Practical experience with airfoil optimization techniques has revealed unexpected diculties. Traditionally the performance of an airfoil is optimized for given, or assumed, model parameters. Experience has

indicated that a deterministic optimization for discrete operating conditions may result in dramatically inferior performance when the actual conditions are dierent from these, somewhat arbitrarily chosen, design

values. Extensions to multi-point optimization have proven unable to adequately remedy the problem of

\localized optimization". This paper presents an intrinsically statistical approach and demonstrates how the

shortcomings of multi-point optimization with respect to \localized optimization" can be overcome.

Luttgen, Gerald, and Walter Vogler: A faster-than relation for asynchronous processes. ICASE Report No.

2001-2, (NASA/CR-2001-210651), January 16, 2001, 35 pages. To be submitted to the 12th International

Conference on Concurrency Theory. This paper introduces a novel (bi)simulation-based faster-than preorder which relates asynchronous

processes with respect to their worst-case timing behavior. The studies are conducted for a conservative

36
extension of the process algebra CCS, called TACS, which permits the specication of maximal time bounds

of actions. TACS complements work in plain process algebras which compares asynchronous processes with

respect to their functional reactive behavior only, and in timed process algebras which focus on analyzing

synchronous processes. The most unusual contribution of this paper is in showing that the proposed fasterthan preorder coincides with two other and at least equally appealing preorders, one of which considers the

absolute times at which actions occur in system runs. The paper also develops the semantic theory of TACS:

it characterizes the largest precongruence contained in the faster-than preorder. A small example relating

two implementations of a simple storage system testies to the practical utility of the new theory. Mavriplis, Dimitri J.: Multigrid approaches to non-linear diusion problems on unstructured meshes. ICASE

Report No. 2001-3, (NASA/CR-2001-210660), February 12, 2001, 16 pages. Submitted to the Journal of

Numerical Linear Algebra with Applications.

The eciency of three multigrid methods for solving highly non-linear diusion problems on twodimensional unstructured meshes is examined. The three multigrid methods dier mainly in the manner in

which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the nonlinear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a

linear solver on each level as a smoother. Results indicate that all methods are equally eective at converging

the non-linear residual in a given number of grid sweeps, but that the linear solver is more ecient in cpu

time due to the lower cost of linear versus non-linear grid sweeps.

Povitsky, Alex, and Manuel D. Salas: Lagrangian approach to jet mixing and optimization of the reactor for

production of carbon nanotubes. ICASE Report No. 2001-4, (NASA/CR-2001-210662), February 14, 2001,

27 pages. To be submitted to AIAA Journal.

This study was motivated by an attempt to optimize the High Pressure carbon oxide (HiPco) process

for the production of carbon nanotubes from gaseous carbon oxide. The goal is to achieve rapid and uniform

heating of catalyst particles by an optimal arrangement of jets. A mixed Eulerian and Lagrangian approach

is implemented to track the temperature of catalyst particles along their tra jectories as a function of time.

The FLUENT CFD software with second-order upwind approximation of convective terms and an algebraic multigrid-based solver is used. The poor performance of the original reactor conguration is explained in

terms of features of particle tra jectories. The tra jectories most exposed to the hot jets appear to be the most

problematic for heating because they either bend towards the cold jet interior or rotate upwind of the mixing

zone. To reduce undesirable slow and/or oscillatory heating of catalyst particles, a reactor conguration with

three central jets is proposed and the optimal location of the central and peripheral nozzles is determined.

Ciardo, Gianfranco, Gerald Luttgen, and Radu Siminiceanu: Saturation: An ecient iteration strategy for

symbolic state-space generation. ICASE Report No. 2001-5, (NASA/CR-2001-210663), February 14, 2001,

21 pages. To appear in Proc. of the 7th Int'l. Conf. on Tools and Algorithms for the Construction and

Analysis of Systems.

This paper presents a novel algorithm for generating state spaces of asynchronous systems using Multi- valued Decision Diagrams. In contrast to related work, the next-state function of a system is not encoded

37
as a single Boolean function, but as cross-products of integer functions. This permits the application of various iteration strategies to build a system's state space. In particular, this paper introduces a new elegant

strategy, called saturation, and implements it in the tool SMART. On top of usually performing several

orders of magnitude faster than existing BDD-based state-space generators, the algorithm's required peak

memory is often close to the nal memory needed for storing the overall state spaces.

Hesthaven, J.S., and T. Warburton: High-order/spectral methods on unstructured grids I. Time-domain

solution of Maxwel l's equations. ICASE Report No. 2001-6, (NASA/CR-2001-210836), March 27, 2001, 45

pages. Submitted to the Journal of Computational Physics.

We present an ab initio development of a convergent high-order accurate scheme for the solution of linear

conservation laws in geometrically complex domains. As our main example we present a detailed development

and analysis of a scheme suitable for the time-domain solution of Maxwell's equations in a three-dimensional

domain. The fully unstructured spatial discretization is made possible by the use of a high-order nodal basis,

employing multivariate Lagrange polynomials dened on the triangles and tetrahedra. Careful choices of

the unstructured nodal grid points ensure high-order/spectral accuracy, while the equations themselves are

satised in a discontinuous Galerkin form with the boundary conditions being enforced weakly through a

penalty term. Accuracy, stability, and convergence of the semi-discrete approximation to Maxwell's equations

is established rigorously and bounds on the global divergence error are provided. Concerns related to ecient

implementations are discussed in detail.

This sets the stage for the presentation of examples, verifying the theoretical results, as well as illustrating

the versatility, 
exibility, and robustness when solving two- and three-dimensional benchmarks in computational electromagnetics. Pure scattering as well as penetration is discussed and high parallel performance of

the scheme is demonstrated.

38
INTERIM REPORTS

Rubinstein, R., C.L. Rumsey, M.D. Salas, and J.L. Thomas, editors, Turbulence modeling workshop. ICASE

Interim Report No. 37, (NASA/CR-2001-210841), April 11, 2001, 193 pages.

Advances in turbulence modeling are needed in order to calculate high Reynolds number 
ows near the

onset of separation and beyond. To this end, the participants in this workshop made the following recommendations. (1) A national/international database and standards for turbulence modeling assessment should

be established. Existing experimental data sets should be reviewed and categorized. Advantage should be

taken of other eorts already underway, such as that of the European Research Community on Flow, Turbulence, and Combustion (ERCOFTAC) consortium. Carefully selected \unit" experiments will be needed,

as well as advances in instrumentation, to ll the gaps in existing datasets. A high priority should be given

to document existing turbulence model capabilities in a standard form, including numerical implementation

issues such as grid quality and resolution. (2) NASA should support long-term research on Algebraic Stress

Models and Reynolds Stress Models. The emphasis should be placed on improving the length-scale equation,

since it is the least understood and is a key component of two-equation and higher models. Second priority

should be given to the development of improved near-wall models. Direct Numerical Simulations (DNS) and

Large Eddy Simulations (LES) would provide valuable guidance in developing and validating new Reynoldsaveraged Navier-Stokes (RANS) models. Although not the focus of this workshop, DNS, LES, and hybrid

methods currently represent viable approaches for analysis on a limited basis. Therefore, although computer

limitations require the use of RANS methods for realistic congurations at high Reynolds number in the

foreseeable future, a balanced eort in turbulence modeling development, validation, and implementation

should include these approaches as well.

39
OTHER REPORTS

Ambur, D.R., N. Jaunky, C.D. Davila, and M.W. Hilburger, \Progressive failure studies of composite panels

with and without cutouts," AIAA Paper 2001-1182, presented at the 42nd AIAA/ASME/ASCE/AHS/ASC

Structures, Structural Dynamics, and Materials Conference, Seattle, WA.

Bogetti, T.A., V.M. Harik, C.P.R. Hoppel, J. Newill, and B. Burns, \Prediction of the nonlinear response

and failure of composite laminates," Composites Science and Technology, Special Issue on the International

Exercise on Failure of Composites, 2001, in press.

Harik, V.M., \Optimization of structural designs for a safe failure pattern: Layered material systems,"

Materials and Design, May 2001, to appear.

Harik, V.M., and R.A. Cairncross, \Formation of interfacial voids in composites with a weakly bonded

viscoplastic matrix," Mechanics of Materials, 32 (December 2000), pp. 807{820.

Harik, V.M., J.R. Klinger, and T.A. Bogetti, \Low cycle fatigue of unidirectional composites: Bi-linear S-N

curves," International Journal of Fatigue, 2001, in press.

Harik, V.M., J.R. Klinger, and R.A. Bogetti, \Low cycle fatigue of unidirectional laminates: Stress ratio

eects," ASME Journal of Engineering Materials and Technology, 122 (October 2000), pp. 415{419.

Hart, Roger C., R. Jerey Balla, and G.C. Herring, \Optical measurement of the speed of sound in air over

the temperature range 300-650K," Journal Acoust. Soc. Am., 108 (2000), p. 1946.

Hart, Roger C., R. Jerey Balla, and G.C. Herring, \Simultaneous velocimetry and thermometry of air using

nonresonant heterodyned laser-induced thermal acoustics," App. Opt., 40 (2001), p. 965.

Huyse, L., \Solving problems of optimization under uncertainty as statistical decision problems," AIAA Paper 2001-1519, 42nd AIAA/ASME/ASCE/ASC Structures, Structural Dynamics, and Materials Conference

and Exhibit, Seattle, WA.

Huyse, L., and R.M. Lewis, \Aerodynamic shape optimization of two-dimensional airfoils under uncertain

operating conditions," International Conference on Structural Safety and Reliability, Newport Beach, CA.

Krueger, R., I.L. Paris, T.K. O'Brien, and P.J. Minguet, \Fatigue life methodology for bonded composite

skin/stringer congurations," ASTM Journal of Composites Technology and Research, submitted January

2001.

Mu~noz, C., R.W. Butler, V. Carreno, and G. Dowek, \On the verication of con
ict detection algorithms,"

NASA Technical Memorandum, submitted March 2001.

Ounaies, Z., K. Mossi, R.C. Smith, and J.D. Bernd, \Low-eld and high-eld characterization of THUNDER

actuators," SPIE: Smart Materials and Structures Spring Conference, Newport Beach, CA, March 2001.

40
Ounaies, Z., C. Park, D. Klein, and J.S. Harrison, \Field responsive polyimides: An analysis of their piezoelectricity," American Chemical Society Poly Millennial 2000, December 2000.

Park, C., Z. Ounaies, K. Wise, J.S. Harrison, and J.G. Smith, Jr., \Partially cured polyimides: A poling

study," American Chemical Society Poly Millennial 2000, December 2000.

Povitsky, A., \Aeroacoustics of a stagnation 
ow near a rigid wall," Physics of Fluids, 12, No. 10 (2000),

pp. 2595{2608.

Povitsky, A., \Cache-friendly algorithm for compact numerical schemes," Applied Mathematics Letters, 14,

No. 4 (2001), pp. 449{454.

Povitsky, A., \High-incidence 3-d lid-driven cavity 
ow," AIAA Paper 2001-2847, 31st AIAA Fluid Dynamics

Conference, June 2001.

Povitsky, A., \High-order compact simulation of wave propagation in a non-uniform mean 
ow," AIAA

Paper 2001-2628, 15th AIAA Computational Fluid Dynamics Conference, Anaheim, CA, June 2001.

Povitsky, A., \Improving jet reactor conguration for production of carbon nanotubes," Computers and

Fluids, accepted, 2001.

Povitsky, A., \Numerical study of wave propagation in a non-uniform compressible 
ow," Physics of Fluids,

submitted.

Povitsky, A., \Parallel ADI solver based on processor scheduling," Applied Mathematics and Computation,

accepted.

Povitsky, A., and M. Salas, \Tra jectory-based approach to jet mixing and optimization of the reactor for

production of carbon nanotubes," Physics of Fluids, submitted.

Stals, Linda, \The parallel solution of radiation transport equations," Proceedings of the Tenth SIAM

Conference on Parallel Processing for Scientic Computing 2001, Portsmouth, VA, March 12{14, 2001.

Wieman, R., T. Kackley, R.C. Smith, Z. Ounaies, and J.D. Bernd, \A displacement model for THUNDER

actuators having general loads and boundary conditions," SPIE: Smart Materials and Structures Spring

Conference, Newport Beach, CA, March 2001.

41
PATENTS

Dingemans, Theo J., Terry L. St. Clair, and Erik S. Weiser, \Liquid crystalline thermosets from oligo-esters,

ester-imides, and ester-amides," led in January 2001.

Su, Ji, Joycelyn S. Harrison, Terry L. St. Clair, and Zoubieda Ounaies, \Piezoelectric-electrostrictive Polymeric Blends for Sensor and Actuation Dual Functionality," Invention Disclosure led November 6, 2000.

42
ICASE COLLOQUIA

Name/Aliation/Title Date

Philip Hall, Imperial College, UK October 3, 2000

\Chaotic Breakdown of Stagnation Point Flows"

Enrique Lavernia, University of California, Irvine October 5, 2000

\Processing of Nanostructured Systems: Coatings and Bulk Materials"

Julia Weertman, Northwestern University October 18, 2000

\Mechanical Behavior of Nanocrystalline Metals"

Robert Averback, University of Illinois at Urbana-Champaign October 19, 2000

\Processing and Properties of Nanostructured Bulk Metallic Alloys"

Ira Livshits, Carnegie Mellon University October 20, 2000

\Wave-ray Multigrid Methods for Highly Indenite Helmholtz Equation"

Oren Livne, Weizmann Institute of Science, Israel October 23, 2000

\O(N log N) Multilevel Calculation of N Eigenfunctions"

Gary Shi
et, University of Virginia October 26, 2000

\Nanocrystal Formation from Aluminum-based Metallic Glass"

Michael Krane, Rutgers University October 27, 2000

\Reduced-complexity Aeroacoustic Prediction in Pipe Flows Applied to

Speech Synthesis"

Bjorn Backman, University of Southern Florida November 13, 2000

ICASE Series on Risk-Based Design: \Design Innovation and Risk

Management: A Structural Designer's Voyage Into Uncertainty"

Raymond Cosner, Boeing Phantom Works, St. Louis, MO November 14, 2000

ICASE Series on Risk-based Design: \Uncertainty Management in

Computational Fluid Dynamics"

Jianjun Cheng, University of California, Santa Barbara November 15, 2000

\Synthesis and Studies of Optically Active Poly(beta-peptides)"

Kamen Beronov, Nagoya University, Japan November 16, 2000

\Three Topics in Two-point Closure Modeling of Anisotropic Homogeneous

Turbulence"

43
Name/Aliation/Title Date

Maher Boulos, Universite de Sherbrooke, Quebec, Canada November 17, 2000

\Thermal Plasma Applications to Nano-structured Materials Synthesis"

Takashi Ishihara, Nagoya University, Japan November 17, 2000

\Lagrangian Statistics in the Inertial Subrange of Isotropic Turbulence"

David Nicholls, University of Minnesota November 20, 2000

\High Order Boundary Perturbation Methods for Free Boundary and

Boundary Value Problems"

Anatole Beck, University of Wisconsin, Madison November 21, 2000

\A Fractal Example in Ordinary Dierential Equations"

Zhenyuan Wang, University of Texas at El Paso December 1, 2000

\Classication by Nonlinear Integral Pro jection Pursuit"

Singiresu Rao, University of Miami December 4, 2000

ICASE Series on Risk-based Design: \Modeling of Uncertainty in Structural

Design"

Gilbert Strang, Massachusetts Institute of Technology December 15, 2000

\Three Matrices and Their Applications"

Hanne Gottliebsen, University of St. Andrews January 16, 2001

\Transcendental Functions and Continuity Checking in PVS"

Nahum Zobin, The College of William & Mary January 17, 2001

\Math of Heart Attacks"

Scott Beeler, North Carolina State University January 22, 2001

\Nonlinear Feedback Control Methodologies and Their Application to a Thin

Film Growth Process"

Timothy Hasselman, ACTA Incorporated January 25, 2001

ICASE Series on Risk-based Design: \Reliability-based Optimization for

Structural Design"

Seongsin Kim, Agilent Technologies, San Jose, CA January 29, 2001

\MOCVD Growth and Characterization of Epitaxial Quantum Dots for

Optoelectronic Devices"

44
Name/Aliation/Title Date

Dennis Gannon, Indiana University, Bloomington February 2, 2001

\Science Portals and Distributed Software Component Architectures"

Sarah-Jane Frankland, North Carolina State University February 9, 2001

\Evaluating Carbon Nanotube Applications with Simulation: Hydrogen

Storage and Polymer Composites"

William Oberkampf, Sandia National Laboratories February 21, 2001

ICASE Series on Risk-based Design: \Error and Uncertainty in Modeling

and Simulation"

Billie F. Spencer, The University of Notre Dame February 26, 2001

ICASE Series on Risk-based Design: \Control of Civil Infrastructure

Systems"

Christopher Viney, Heriot-Watt University, Scotland March 1, 2001

\New Materials from the Zoo"

Matthias Heinkenschloss, Rice University March 9, 2001

\Domain Decomposition Based Optimization Methods for the Optimal

Control of Partial Dierential Equations"

Boris Chernyavskiy, Rutgers, The State University of New Jersey March 14, 2001

\Parallel Code Performance on Beowulf Type Clusters"

Semyon Tsynkov, North Carolina State University March 15, 2001

\Active Shielding and Control of Environmental Noise"

S. Hariharan, The University of Akron March 16, 2001

\On Phase-eld Methods"

Svetlana Poroseva, Stanford University March 19, 2001

\Pressure-containing Correlations: The Main Issue in High-order Turbulence

Closures"

Pin Tong, Hong Kong University of Science and Technology March 23, 2001

\Fracture of Piezoelectric Ceramics"

45
OTHER ACTIVITIES

On January 12{13, 2001, ICASE and NASA Langley co-sponsored a Turbulence Modeling Workshop

at the Reno Hilton in Reno, Nevada. The purpose of the Workshop was to discuss current and future

capabilities for predicting High Reynolds Number turbulent separated 
ows at 
ight conditions. There were

39 attendees, and an ICASE Interim Report will be published.

46
ICASE STAFF

I. ADMINISTRATIVE

Manuel D. Salas, Director, M.S., Aeronautics and Astronautics, Polytechnic Institute of Brooklyn, 1970.

Fluid Mechanics and Numerical Analysis.

Linda T. Johnson, Oce and Financial Administrator

Barbara A. Cardasis, Administrative Secretary

Etta M. Morgan, Accounting Supervisor

Emily N. Todd, Conference Manager/Executive Assistant

Shannon K. Verstynen, Information Technologist

Gwendolyn W. Wesson, Contract Accounting Clerk

Shouben Zhou, Systems Manager

Peter J. Kearney, Coral Manager/Assistant Systems Manager (Through February 2001)

J. Ryan Cresawn, Systems Manager for Coral and the ICASE Computational Grid/Assistant Systems Manager (Beginning March 2001)

II. SCIENCE COUNCIL

David Gottlieb, (Chair) Professor, Division of Applied Mathematics, Brown University. Lee Beach, Professor, Department of Physics, Computer Science & Engineering, Christopher Newport Uni- versity.

Jack Dongarra, Distinguished Professor, Department of Computer Science, University of Tennessee.

Joseph E. Flaherty, Amos Eaton Professor, Departments of Computer Science and Mathematical Sciences,

Rensselaer Polytechnic Institute.

Forrester Johnson, Aerodynamics Research, Boeing Commercial Airplane Group.

John C. Knight, Professor, Department of Computer Science, School of Engineering and Applied Science,

University of Virginia.

Robert W. MacCormack, Professor, Department of Aeronautics and Astronautics, Stanford University.

Stanley G. Rubin, Professor, Department of Aerospace Engineering and Engineering Mechanics, University

of Cincinnati.

Manuel D. Salas, Director, ICASE, NASA Langley Research Center.

47
III. RESEARCH FELLOWS

Dimitri Mavriplis - Ph.D., Mechanical and Aerospace Engineering, Princeton University, 1988. Applied &

Numerical Mathematics [Grid Techniques for Computational Fluid Dynamics]. (February 1997 to August

2003)

Josip Loncaric - Ph.D., Applied Mathematics, Harvard University, 1985. Applied & Numerical Mathematics

[Multidisciplinary Design Optimization]. (March 2001 to August 2002)

IV. SENIOR STAFF SCIENTISTS

Brian G. Allan - Ph.D., Mechanical Engineering, University of California at Berkeley, 1996. Applied &

Numerical Mathematics [Multidisciplinary Design Optimization]. (February 1996 to November 2003)

Thomas M. Eidson - Ph.D., Mechanical Engineering, University of Michigan, 1982. Computer Science

[Distributed Computing]. (October 2000 to September 2003)

Alfons E. Geser - Ph.D., Computer Science, University of Passau, Germany, 1991. Computer Science [Formal

Methods]. (January 2001 to December 2002)

Roger C. Hart - Ph.D., Physics, University of Tennessee, 1991. Fluid Mechanics [Measurement Science and

Technology]. (December 1998 to October 2001)

Guowei He - Ph.D., Theoretical and Applied Mechanics, Northwestern Polytechnic University, Xian, China,

1991. Fluid Mechanics [Turbulence Modeling and Direct Numerical Simulation]. (July 2000 to June 2003)

Navin Jaunky - Ph.D., Mechanical Engineering, Old Dominion University, 1995. Structures & Materials

[Composite Structural Damage Tolerance and Residual Strength Methodologies. (January 2001 to December

2002)

Josip Loncaric - Ph.D., Applied Mathematics, Harvard University, 1985. Applied & Numerical Mathematics

[Multidisciplinary Design Optimization]. (March 1996 to February 2001)

Li-Shi Luo - Ph.D., Physics, Georgia Institute of Technology, 1993. Computer Science [Parallel Algorithms].

(November 1996 to August 2002)

Zoubeida Ounaies - Ph.D., Engineering Science and Mechanics, The Pennsylvania State University, 1995.

Structures & Materials [Characterization of Advanced Piezoelectric Materials]. (March 1999 to November

2002)

Alexander Povitsky - Ph.D., Mechanical Engineering, Moscow Institute of Steel and Alloys Technology

(MISA), Russia, 1988. Computer Science [Parallelization and Formulation of Higher Order Schemes for

Aeroacoustics Noise Propagation]. (October 1997 to August 2001)

David Sidilkover - Ph.D., Applied Mathematics, The Weizmann Institute of Science, 1989. Applied &

Numerical Mathematics [Numerical Analysis and Algorithms]. (November 1994 to February 2001)

48
V. SCIENTIFIC STAFF

Scott C. Beeler - Ph.D., Applied Mathematics, North Carolina State University, 2000. Applied & Numerical

Mathematics [Nonlinear Suboptimal Feedback Control]. (March 2001 to February 2003)

Theodorus Dingemans - Ph.D., Organic Chemistry, University of North Carolina at Chapel Hill, 1998.

Structures & Materials. (September 2000 to August 2002)

Boris Diskin - Ph.D., Applied Mathematics, The Weizmann Institute of Science, Israel, 1998. Applied &

Numerical Mathematics [Convergence Acceleration]. (July 1998 to September 2002)

Vasyl M. Harik - Ph.D., Mechanical Engineering, University of Delaware, 1997; Ph.D. equiv., Engineering Physics, Moscow State University, 1993. Structures & Materials [Composites and Failure Mechanics].

(October 2000 to October 2002)

Luc Huyse - Ph.D., Civil Engineering, Structures, University of Calgary, Canada, 1999. Applied & Numerical

Mathematics [Managing Uncertainties in Multidisciplinary Research]. (October 1999 to August 2001)

Ronald Krueger - Ph.D., Aerospace Engineering, University of Stuttgart, Germany, 1996. Structures &

Materials [Analysis of Composite Delamination of Structures]. (August 2000 to August 2002)

Cesar A. Mu~noz - Ph.D., Computer Science, University of Paris 7, 1997. Computer Science [Formal Methods

Research for Safety Critical Systems]. (May 1999 to April 2002)

Lee M. Nicholson - Ph.D., Materials Science, University of Cambridge, United Kingdom, 1997. Structures

& Materials [Computational Nanotechnolgy]. (May 2000 to May 2003)

Cheol Park - Ph.D., Macromolecular Science and Engineering, The University of Michigan, 1997. Structures

& Materials [Electro-active Materials]. (November 2000 to October 2002)

Won J. Yi - Ph.D., Electrical Engineering, University of Nebraska, 1997. Structures & Materials [Smart

Materials and Flow Control]. (February 2001 to February 2003)

VI. VISITING SCIENTISTS

Gilles A. Dowek - Ph.D., Computer Science, University of Paris 7, 1991. Research Scientist, Institut National

de Recherche en Informatique et en Automatique (INRIA). Computer Science [Formal Methods]. (January

2001 to April 2001)

Kab Seok Kang - Ph.D., Mathematics, Korea Advanced Institute of Science & Technology, 1999. Postdoctoral Research Scientist, Korea Advanced Institute of Science & Technology. Applied & Numerical

Mathematics [Multigrid Algorithms for Partial Dierential Equations Discretized on Unstructured Grids].

(February 2001 to January 2002)

Sun Mok Paik - Ph.D., Physics, University of Maryland, 1988. Assistant Associate Professor, Department of

Physics, Kangwon National University, Korea. Structures & Materials [Computational Materials]. (February

2000 to July 2001)

49
Jong-Yeob Shin - Ph.D., Aerospace Engineering, University of Minnesota, 2000. Research Assistant, Uni- versity of Minnesota. Applied & Numerical Mathematics [Advanced Control Methods]. (November 2000 to

October 2002)

J. Raymond Skarda - Ph.D., Mechanical and Aerospace Engineering, Case Western Reserve University, 1996.

Fluid Mechanics [Gravity Flows]. (August 2000 - February 2001)

Linda Stals - Ph.D., Mathematics, Australian National University, 1996. Assistant Professor, Department

of Computer Science, Old Dominion University. Computer Science [Parallel Implicit Multilevel Algorithms].

(November 1998 to October 2001)

VII. SHORT-TERM VISITING SCIENTISTS

Xuesong Wu - Ph.D., Applied Mathematics, Imperial College, London, 1992. Senior Lecturer, Department of

Mathematics, Imperial College, London. Fluid Mechanics [Modeling of Unsteady Flow Phenomena] (March

2001 to April 2001)

VIII. ASSOCIATE RESEARCH FELLOW

David E. Keyes - Ph.D., Applied Mathematics, Harvard University, 1984. Computer Science [Parallel Numerical Algorithms]

IX. CONSULTANTS

Saul Abarbanel - Ph.D., Theoretical Aerodynamics, Massachusetts Institute of Technology, 1959. Professor,

Department of Applied Mathematics, Tel Aviv University, Israel. Applied & Numerical Mathematics [Global

Boundary Conditions for Aerodynamics and Aeroacoustic Computations]

H. Thomas Banks - Ph.D., Applied Mathematics, Purdue University, 1967. Professor, Department of Mathematics, Center for Research in Scientic Computations, North Carolina State University. Applied & Numerical Mathematics [Control Theory]

Przemyslaw Bogacki - Ph.D., Mathematical Sciences, Southern Methodist University, 1990. Assistant Professor, Department of Mathematics and Statistics, Old Dominion University. Applied & Numerical Mathematics

[High Performance Methods in Nontraditional CFD]

Achi Brandt - Ph.D., Mathematics, The Weizmann Institute of Science, 1965. Professor, Department of

Applied Mathematics, The Weizmann Institute of Science, Israel. Applied & Numerical Mathematics [Con- vergence Acceleration]

Thomas W. Crockett - B.S., Mathematics, The College of William & Mary, 1977. Senior Research Associate,

Computational Science Cluster, The College of William & Mary. Computer Science [Scientic Visualization]

50
Ayodeji O. Demuren - Ph.D., Mechanical Engineering, Imperial College London, United Kingdom, 1979.

Associate Professor, Department of Mechanical Engineering and Mechanics, Old Dominion University. Fluid

Mechanics [Numerical Modeling of Turbulent Flows]

Dave E. Eckhardt - Ph.D., Computer Science, George Washington University, 1978. Retired. Computer

Science [Operational Concepts of National Aerospace System Needs]

Sharath Girima ji - Ph.D., Mechanical Engineering, Cornell University, 1990. Associate Professor, Department of Aerospace Engineering, Texas A&M University. Fluid Mechanics [Turbulence and Combustion]

David Gottlieb - Ph.D., Numerical Analysis, Tel-Aviv University, Israel, 1972. Ford Foundation Professor &

Chair, Division of Applied Mathematics, Brown University. Applied & Numerical Mathematics [Boundary

Conditions for Hyperbolic Systems]

Jan S. Hesthaven - Ph.D., Applied Mathematics/Numerical Analysis, Technical University of Denmark, 1995.

Visiting Assistant Professor, Division of Applied Mathematics, Brown University. Applied & Numerical

Mathematics [Computational Electromagnetics]

Fang Q. Hu - Ph.D., Applied Mathematics, Florida State University, 1990. Assistant Professor, Department

of Mathematics and Statistics, Old Dominion University. Fluid Mechanics [Aeroacoustics]

Frank Kozusko - Ph.D., Computational and Applied Mathematics, Old Dominion University, 1995. Assistant

Professor, Department of Mathematics, Hampton University. Fluid Mechanics [Airfoil Design]

David G. Lasseigne - Ph.D., Applied Mathematics, Northwestern University, 1985. Assistant Professor,

Department of Mathematics and Statistics, Old Dominion University. Fluid Mechanics [Asymptotic and

Numerical Methods for Computational Fluid Dynamics]

R. Michael Lewis - Ph.D., Mathematical Sciences, Rice University, 1989. Assistant Professor, Department of

Applied Mathematics, The College of William & Mary. Applied & Numerical Mathematics [Multidisciplinary

Optimization and Managing Uncertainties]

Wu Li - Ph.D., Mathematics, The Pennsylvania State University, 1990. Associate Professor, Department of

Mathematics and Statistics, Old Dominion University. Applied & Numerical Mathematics [Optimization]

Gerald Luttgen - Ph.D., Computer Science, University of Passau, Germany, 1998. Professor, Department of

Computer Science, The University of Sheeld, United Kingdom. Computer Science [Formal Methods]

James E. Martin - Ph.D., Applied Mathematics, Brown University, 1991. Assistant Professor, Department

of Mathematics, Christopher Newport University. Fluid Mechanics [Turbulence and Computation]

Karla Mossi - Ph.D., Mechanical Engineering, Old Dominion University, 1998. Assistant Professor, Department of Mechanical Engineering, Virginia Commonwealth University. Structures & Materials [Electro Active

Materials]

Jan Nordstrom - Ph.D., Numerical Analysis, Uppsala University, Sweden, 1993. Senior Scientist, The Aeronautical Research Institute of Sweden. Applied & Numerical Mathematics [Global Boundary Conditions for

Aerodynamic and Aeroacoustic Computations]

51
Devendra Parmar - Ph.D., Condensed Matter Physics, Aligarh Muslim University, India, 1974. Research

Professor, Department of Mechanical Engineering, Old Dominion University. Fluid Mechanics [Literature

Survey for Space Instrumentation]

Merrell L. Patrick - Ph.D., Mathematics, Carnegie Institute of Technology, 1964. Retired. Computer Science

Alex Pothen - Ph.D., Applied Mathematics, Cornell University, 1984. Professor, Department of Computer

Science, Old Dominion University. Computer Science [Parallel Numerical Algorithms]

Chi-Wang Shu - Ph.D., Mathematics, University of California-Los Angeles, 1986. Associate Professor, Division of Applied Mathematics, Brown University. Fluid Mechanics [Computational Aeroacoustics]

Ralph C. Smith - Ph.D., Mathematics, Montana State University, 1990. Professor, Department of Mathematics, North Carolina State University. Applied & Numerical Mathematics [Optimal Control Techniques

for Structural Acoustics Problems]

Virginia Torczon - Ph.D., Mathematical Sciences, Rice University, 1989. Assistant Professor, Department of

Computer Science, The College of William & Mary. Computer Science [Parallel Algorithms for Optimization

Including Multidisciplinary Optimization]

Semyon V. Tsynkov - Ph.D., Computational Mathematics, Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, 1991. Senior Lecturer, Department of Applied Mathematics, Tel Aviv University, Israel. Applied & Numerical Mathematics [Global Boundary Conditions for Aerodynamic and Aeroacoustic

Computations]

Michael Wagner - Ph.D., Mathematical Programming, Cornell University, 2000. Assistant Professor, Department of Mathematics & Statistics, Old Dominion University. Applied & Numerical Mathematics [Applied

Optimization] (September 2000 to September 2001)

Mohammad Zubair - Ph.D., Computer Science, Indian Institute of Technology, Delhi, India, 1987. Professor,

Department of Computer Science, Old Dominion University. Computer Science [Performance of Unstructured Flow-solvers on Multi-processor Machines]

X. GRADUATE STUDENTS

Ahmed H. Al-Theneyan - Department of Computer Science, Old Dominion University. (May 1999 to December 2000)

Abdelkader Baggag - Department of Computer Science, Hampton University. (September 1995 to Present)

Gregory Hicks - Department of Applied Mathematics, Center for Research in Scientic Computations, North

Carolina State University. (September 2000 to Present)

Jianing Huang - Department of Computer Science, Old Dominion University. (September 2000 to Present)

Amol Jakatdar - Department of Computer Science, Old Dominion University. (May 2000 to Present)

52
Michele Joyner - Department of Applied Mathematics, Center for Research in Scientic Computations, North

Carolina State University. (September 2000 to Present)

Mohamed Kholief - Department of Computer Science, Old Dominion University. (August 2000 to Present)

Brahmadatt Koodallur - Department of Computer Science, Old Dominion University. (August 2000 to

Present)

Jun Liao - Department of Aerospace Engineering, University of Florida. (March 2001 to Present)

Yawei Li - Department of Aerospace Engineering, Mechanics and Engineering Sciences, University of Florida.

(January 2000 to March 2001)

Seth D. Milder - Department of Physics and Astronomy, George Mason University. (September 1997 to

Present)

Kara S. Olson - Department of Computer Science, Old Dominion University. (January 1999 to Present)

Juan A. Pelaez - Department of Aerospace Engineering, Old Dominion University. (March 1999 to March

2001)

Dazhi Yu - Department of Aerospace Engineering, Mechanics and Engineering Sciences, University of Florida.

(January 2000 to December 2000)

Min Yue - Department of Computer Science, Old Dominion University. (January 2001 to Present)

53