automated approach to very high order aeroacoustic computations computational aeroacoustics requires efficient high resolution simulation tools for smooth problems this is best accomplished with very high order in space and time methods on small stencils however the complexity of highly accurate numerical methods can inhibit their practical application especially in irregular geometries this complexity is reduced by using a special form of hermite divided difference spatial interpolation on cartesian grids and a cauchy kowalewski recursion procedure for time advancement in addition a stencil constraint tree reduces the complexity of interpolating grid points that am located near wall boundaries these procedures are used to develop automatically and to implement very high order methods 15 for solving the linearized euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point the accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries

interface conditions of finite difference compact schemes for computational aeroacoustics the interface condition provides flexibility to handle complex geometries on a set of structured grids however when used with a compact scheme to apply in computational aeroacoustics its accuracy and stability may be degraded seriously by the boundary treatment that arises at a grid interface to minimize this effect a modified characteristic condition is incorporated in the finite difference compact scheme by using an explicit difference form at the boundary the extension of this approach is naturally attained through the coordinate transformation of convective terms across an interface in multidimensions the validity of current development is demonstrated through a simulation of trailing edge noise generation from an airfoil at a low mach number

cartesian boundary treatment of curved walls for high order computational aeroacoustics schemes it is known that the use of high order central difference schemes on a cartesian grid is preferable for the computation of acoustic wave propagation problems those schemes tend to be less dispersive and dissipative than most other types of schemes they are also more capable of providing an accurate wave speed a cartesian boundary treatment for problems involving the scattering of acoustic waves by solid objects with curved boundary surfaces designed to be used in conjunction with such high order central difference schemes is proposed the development of this method is based on the observation that a solid wall actually exerts a pressure force on the fluid to keep it from flowing across the wall surface in this method ghost values of pressure are introduced at mesh points adjacent to the solid boundary inside the object the ghost values are then chosen so that the solid wall boundary condition is satisfied the method is also applicable to objects with sharp corners numerical examples are provided

improved block interface conditions for aeroacoustic problems with grid discontinuities aeroacoustic simulations are extremely sensitive to numerical errors to achieve a high order of accuracy optimized finite difference schemes such as the well known dispersion relation preservation schemes and multiblock structured meshes are often used challenges appear in communicating the flow information near grid discontinuities between neighboring blocks and sophisticated interface treatments are required the characteristic interface condition has been successful in applications in previous publications and yet limitations exist that are identified in the present study this paper proposes a new interface treatment based on the analogy between finite difference and finite volume discretizations one sided finite difference schemes are used to calculate the spatial derivatives in the normal direction and the residuals are reconstructed from a finite volume perspective applications to several benchmark cases show an encouraging improvement as compared to the previous characteristic interface

computation of subsonic inviscid flow past a cone using high order schemes a wake dominated unsteady flow of mach number 0 2 past a cone of vertex angle 60 deg is calculated numerically using high order finite difference schemes on structured grids the three dimensional compressible euler equations are solved to simulated an inviscid flow that exhibits large fluctuations of pressure and velocity as a result of the shedding of vortices behind the cone an axisymmetric structured grid system is used it is generated by rotating a two dimensional grid plane around a centerline the grid singularity at the centerline where the jacobian and some grid metrics approach infinity is avoided by changing the form of the flux vectors in the euler equations without any asympotic assumption or simplification fourth and sixth order finite difference schemes are used for the evaluation of spatial derivatives and a fourth order runge kutta scheme is used for marching the solution in time the complex wake structures and motions behind the cone are investigated by visualizing the vorticity field the mean flow pattern and periodic phenomena are analyzed and compared with experimental data this demostrates the accuracy of the present approach to further analyses of wake dominated flows past axisymmetric blunt based bodies

variance balanced change over designs for dependent observations we show that variance balanced change over designs can be obtained from orthogonal arrays for many dependence structures some examples and design comparisons are given

patched characteristic interface condition for high order multiblock aeroacoustic computation a patched grid technique is proposed with the aim of increasing the flexibility and efficiency of high order finite difference schemes for multiblock computational aeroacoustics the patched characteristic interface conditions allow arbitrarily positioned nonmatching grid points along each side of the internal block boundaries the work extendsthecharacteristicinterfaceconditionsoriginally proposedtotreattheproblemofgridsingularityassociated with structured grids and high order finite difference schemes a simple method of generalizing the original characteristic interface conditions theory for arbitrary block coordinate alignments is also outlined the new interface condition is implemented into a high order computational aeroacoustics code to solve either the euler or navier stokes equations the patch algorithm makes use of a high order optimized interpolation method to approximatethecharacteristicconvectiontermsatcorrespondinglocationsalongtheblockinterface theresultisan interface condition that provides better management of cell distribution in the computational domain while at the same time providing a treatment to the grid singularity problem associated with complex geometries several test casesareusedtodemonstratethe flexibilityofthenewinterfaceconditionandtoinvestigatevariousparameters the computed results are shown to be in excellent agreement with exact solutions

distributed lagrange multiplier methods for incompressible viscous flow around moving rigid bodies abstract in this article we discuss the application of a distributed lagrange multiplier based fictitious domain method to the numerical simulation of incompressible viscous flow modelled by the navier stokes equations around moving bodies we suppose the rigid bodies motion known a priori the solution method combines finite element approximations time discretization by operator splitting and conjugate gradient algorithms for the solution of the linearly constrained quadratic minimization problems coming from the splitting method numerical experiment results for two dimensional flow around a moving disk are presented

on optimal crossover designs when carryover effects are proportional to direct effects there are a number of different models for crossover designs which take account of carryover effects since it seems plausible that a treatment with a large direct effect should generally have a larger carryover effect kempton et al 2001 considered a model where the carryover effects are proportional to the direct effects the advantage of this model lies in the fact that there are fewer parameters to be estimated its problem lies in the nonlinearity of the estimators kempton et al 2001 considered the least squares estimator they point out that this estimator is asymptotically equivalent to the estimator in a linear model which assumes the true parameters to be known for this estimator they determine optimal designs numerically for some cases the present paper generalises some of their results our results are derived with the help of a generalisation of the methods used in kunert martin 2000

adjoint based optimization of particle trajectories in laminar flows we present a performant numerical algorithm for the optimal control of particle controls in low reynolds number flows in particular circular particles with mass are considered an optimal control problem for the particle trajectories is presented which is solved by means of a steepest descent algorithm here the derivative information is obtained using adjoint calculus finally numerical results are presented underlining the feasibility of our approach

radiated noise from airfoils in realistic mean flows the long term objective of the research described is to use computational aeroacoustics methodology and parallel computers to increase the understanding of broadband blade noise in a systematic progression toward simulations of completely realistic configurations and conditions some simplified problems that address the important features of the flow are investigated a two dimensional navier stokes code implemented using the message passing library and fortran 90 on the ibm sp2 is used to perform the calculations results are presented for the interaction of a vortical gust and naca airfoils including nonlinear effects the influence of gust frequency and airfoil thickness is described a multigrid method is used to obtain converged steady state solutions before the gust is introduced in a source region inside the domain

a fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies application to particulate flow abstract in this article we discuss a methodology that allows the direct numerical simulation of incompressible viscous fluid flow past moving rigid bodies the simulation methods rest essentially on the combination of a lagrange multiplier based fictitious domain methods which allow the fluid flow computations to be done in a fixed flow region b finite element approximations of the navier stokes equations occurring in the global model c time discretizations by operator splitting schemes in order to treat optimally the various operators present in the model the above methodology is particularly well suited to the direct numerical simulation of particulate flow such as the flow of mixtures of rigid solid particles and incompressible viscous fluids possibly non newtonian we conclude this article with the presentation of the results of various numerical experiments including the simulation of store separation for rigid airfoils and of sedimentation and fluidization phenomena in two and three dimensions

a distributed lagrange multiplier fictitious domain method for the simulation of flow around moving rigid bodies application to particulate flow in this article we discuss the application of a lagrange multiplier based fictitious domain method to the numerical simulation of incompressible viscous flow modeled by the navier stokes equations around moving rigid bodies the rigid body motion is due to hydrodynamical forces and gravity the solution method combines finite element approximations time discretization by operators splitting and conjugate gradient algorithms for the solution of the linearly constrained quadratic minimization problems coming from the splitting method we conclude this article by the presentation of numerical results concerning the simulation of an incompressible viscous flow around a naca0012 airfoil with a fixed center but free to rotate then the sedimentation of circular cylinders in 2 d channels and finally the sedimentation of spherical balls in cylinders with square cross sections 2000 elsevier science s a all rights reserved

improved grid block interface flux reconstruction method for high order finite difference scheme in this study a new method is proposed to improve the accuracy of the grid block interface flux reconstruction ifr approach which was proposed by the present authors previously for numerical simulation using high order finite difference scheme not only is the flux at the point on the block interface corrected but the fluxes at the adjacent points of the interface are also reconstructed with a selected correction function this improves the accuracy of the ifr method although the biased finite difference scheme is used to compute the spatial derivatives in the interior boundary region four problems including both inviscid and viscous flows are numerically solved with the developed code to validate the accuracy of the improved ifr method the validations imply that the new correction approach improves the accuracy of the ifr method and is effective for inviscid and viscous problems with complex geometry

optimised boundary compact finite difference schemes for computational aeroacoustics a set of optimised boundary closure schemes is presented for use with compact central finite difference schemes in computational aeroacoustics caa involving non trivial boundaries the boundary schemes are given in a form of non central compact finite differences they maintain fourth order accuracy a pentadiagonal matrix system and seven point stencil which the main interior scheme employs this paper introduces a new strategy to optimise the boundary schemes in the spectral domain and achieve the best resolution characteristics given a strict tolerance for the dispersion and dissipation errors the boundary schemes are derived from sophisticated extrapolation of solutions outside the domain the extrapolation functions are devised by combining polynomials and trigonometric series which contain extra control variables used to optimise the resolution characteristics the differencing coefficients of the boundary schemes are determined in association with the existing coefficients of the interior scheme which is also optimised through an improved procedure in this paper the accuracy of the proposed schemes is demonstrated by their application to caa benchmark problems

optimal and efficient repeated measurements designs for uncorrelated observations abstract in repeated measurements crossover or changeover designs experimental subjects units are repeatedly exposed to treatments effects of treatments from one period that extend into the next are called carryover or residual effects in exact design theory designs that are universally optimal in the presence of carryover effects have been found when a subject s responses are uncorrelated however the results are valid only for restricted values of t the number of treatments p the number of periods and n the number of subjects in other optimality results the competing class of designs is a subset of the full class of repeated measurements designs these restrictions hinder applicability in the setting of approximate design theory kushner 1997b developed a new approach valid even for correlated responses here the results are specialized to the case of uncorrelated responses linear equations are given that determine all universally or a and d optimal repeated measurements desig

optimized compact finite difference schemes with maximum resolution direct numerical simulations and computational aeroacoustics require an accurate finite difference scheme that has a high order of truncation and high resolution characteristics in the evaluation of spatial derivatives compact finite difference schemes are optimized to obtain maximum resolution characteristics in space for various spatial truncation orders an analytic method with a systematic procedure to achieve maximum resolution characteristics is devised for multidiagonal schemes based on the idea of the minimization of dispersive phase errors in the wave number domain and these are applied to the analytic optimization of multidiagonal compact schemes actual performances of the optimized compact schemes with a variety of truncation orders are compared by means of numerical simulations of simple wave convections and in this way the most effective compact schemes are found for tridiagonal and pentadiagonal cases respectively from these comparisons the usefulness of an optimized high order tridiagonal compact scheme that is more efficient than a pentadiagonal scheme is discussed for the optimized high order spatial schemes the feasibility of using classical high order runge kutta time advancing methods is investigated

adaptive nonlinear artificial dissipation model for computational aeroacoustics an adaptive nonlinear artificial dissipation model is presented for performing aeroacoustic computations by high order and high resolution numerical schemes based on central finite differences it consists of a selective background smoothing term and a well established nonlinear shock capturing term which damps out spuriousoscillations caused by the central differences in the presence of a shock wave and keeps the linear acoustic waves relatively unaffected a conservative form of the selective background smoothing term is presented to calculate accurate propagation speed or location of the shock wave the nonlinear shock capturing term which has been modeled by second order derivative term is combined with it to improve the resolution of discontinuity and enhance the numerical stability near the shock wave an adaptive control constant for overall amplitude of the dissipation is automatically calculated according to given grid metrics and time dependent flow conditions it is shown that the improved artificial dissipation model reproduces the correct profile and speed of the shock wave suppresses numerical oscillations near the discontinuity and avoids unnecessary damping on the smooth linear acoustic waves the feasibility and performance of the adaptive nonlinear artificial dissipation model for the computational aeroacoustics are investigated and validated by the applications to actual problems

a fictitious domain method for external incompressible viscous flow modeled by navier stokes equations abstract in this article we discuss a fictitious domain method for the numerical solutions of three dimensional elliptic problems with dirichlet boundary conditions and also of the navier stokes equations modeling incompressible viscous flow the methodology for the navier stokes equations described here takes a systematic advantage of time discretization by operator splitting in order to treat separately advection imbedding and incompressibility due to the decoupling fast elliptic solvers can be used to treat the incompressibility condition even if the original problem is taking place on a nonregular geometry the resulting methodology is applied to two dimensional unsteady external incompressible viscous flow problems and three dimensional stokes problems

optimal change over designs when carry over effects are proportional to direct effects of treatments summary we investigate optimal change over designs for a model in which treatment carry over effects are proportional to their direct effects and the proportionality parameter i is unknown a combination of analytical results and computer search is used to identify optimal designs for the estimation of direct effects neighbour balanced designs are shown to have good optimality properties designs with self adjacencies perform better for positive i while those without self adjacencies are better when i is negative the application of the designs to sensory studies is discussed

assessing the impact of carryover effects on the variances of estimators of treatment differences in crossover designs different models that include carryover effects have been studied in the optimal design literature it has been suggested that the use of these models results in increased variances of estimated contrasts of the direct treatment effects leading to inferior estimators in terms of precision under a number of models and selected designs we present variance expressions for the pairwise differences of direct treatment effects and observe that adjusting for carryover effects need not affect the precision of estimators negatively we investigate the existence of designs that produce estimators with relatively small variances under all models considered we conclude that even if a model is not correct it can still be useful in increasing the precision of estimators for treatment contrasts

a fictitious domain finite element method for particulate flows the paper presents a finite element method for the direct numerical simulation of 3d incompressible fluid flows with suspended rigid particles it uses the fictitious domain approach extending the fluid domain into the domain occupied by the particles although the idea for the present formulation came from the fictitious domain formulation of glowinski et al j comput phys 169 2001 363 it finally yielded a new scheme which allows for a more efficient integration of the system of equations and which is easier to implement algorithmically it also avoids the need to grid the rigid particles and solves the entire problem on a single eulerian grid the spatial discretization is performed with p2 p1 finite elements but any other stable pair of approximations can be used the present scheme is compared to a second order scheme based on the approach in glowinski et al loc cit using the test case of a single sphere in a viscous liquid its accuracy costs performance is excellent

characteristic interface conditions for multiblock high order computation on singular structured grid a structured grid with a body usually has a certain point where an abrupt change in the slope of grid line exists the grid metrics are discontinuous at the point because of the discrepancy between the left and the right hand limits of the gradients which leads to grid singularity it may cause serious numerical oscillations especially when high order finite difference schemes are applied to solving conservation form governing equations in generalized coordinates in this paper it is handled by decomposing a computational domain into blocks along the singular lines and imposing interface conditions at the block interfaces for communication between the blocks a set of high order finite difference schemes is used in each block central differences on the interior nodes and one sided differences on the near interface nodes the differencing stencils do not cross the block interfaces and each block is isolated without the singularity which results in no oscillations for the communication between the isolated blocks the interface conditions are newly derived from the characteristic relations of the compressible euler or navier stokes equations the exactness and the feasibility of the interface conditions are investigated for the high order multi block computation on structured grid containing singular points

a priori grid quality estimation for high order finite differencing structured grids using the finite differencing method contain two sources of grid induced truncation errors the first is dependent on the solution field the second is related only to the metrics of the grid transformation the accuracy of the grid transformation metrics is affected by the inverse metrics which are spatial derivatives of the grid in the generalised coordinates the truncation errors contained in the inverse metrics are generated by the spatial schemes fourier analysis shows that the dispersion errors by spatial schemes have similarities to the transfer function of spatial filters this similarity is exploited to define a grid quality metric that can be used to identify areas in the mesh that are likely to generate significant grid induced errors an inviscid vortex convection benchmark case is used to quantify the correlation between the grid quality metric and the solution accuracy for three common geometric features found in grids abrupt changes in the grid metrics skewness and grid stretching a strong correlation is obtained provided that the grid transformation errors are the most significant sources of error

dynamics for controlled navier stokes systems with distributed controls the long time behavior of solutions for an optimal distributed control problem associated with the navier stokes equations is studied first a linear feedback solution for the navier stokes equations is constructed this feedback solution possesses decay in time properties then some preliminary estimates for the long time behavior of all solutions of the navier stokes equations are derived next the existence of a solution for the optimal control problem is proved finally the long time decay properties for the optimal solutions are established

a front tracking method for viscous incompressible multi fluid flows abstract a method to simulate unsteady multi fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described the flow field is discretized by a conservative finite difference approximation on a stationary grid and the interface is explicitly represented by a separate unstructured grid that moves through the stationary grid since the interface deforms continuously it is necessary to restructure its grid as the calculations proceed in addition to keeping the density and viscosity stratification sharp the tracked interface provides a natural way to include surface tension effects both two and three dimensional full numerical simulations of bubble motion are presented

a finite element technique for multifluid incompressible flow using eulerian grids the paper presents a finite element method for 3d incompressible fluid flows with capillary free boundaries it uses a fixed eulerian grid of 10 nodes p2 p1 tetrahedra and tracks the free boundary using a six nodes p2 triangular surface grid in order to improve the mass conservation properties of the method a local enrichment of the finite element basis in the elements intersected by the free boundaries is employed in addition to the surface tracking it also advects a smooth indicator function for an easy identification of the fluid properties in the different parts of the domain the advective part of the navier stokes equations is split and integrated with a characteristic method the remaining generalized stokes problem is resolved by means of an inexact outer inner uzawa iteration with a properly chosen preconditioner the performance of this technique is evaluated on several problems involving droplets in viscous liquids

a front tracking method for the computations of multiphase flow direct numerical simulations of multiphase flows using a front tracking method are presented the method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties interfacial terms are accounted for by adding the appropriate sources as functions at the boundary separating the phases the unsteady navier stokes equations are solved by a conventional finite volume method on a fixed structured grid and the interface or front is tracked explicitly by connected marker points interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid advection of fluid properties such as density is done by following the motion of the front the method has been implemented for fully three dimensional flows as well as for two dimensional and axisymmetric ones first the method is described for the flow of two or more isothermal phases the representation of the moving interface and its dynamic restructuring as well as the transfer of information between the moving front and the fixed grid are discussed applications and extensions of the method to homogeneous bubbly flows atomization flows with variable surface tension solidification and boiling are then presented

optimal repeated measurement designs for a model with partial interactions we consider crossover designs for a model with partial interactions in this model the carryover effect depends on whether the treatment is preceded by itself or not when the aim of the experiment is to study the total effects corresponding to a single treatment we obtain approximate optimal symmetric designs within the competing class of circular designs by generalizing the method introduced by kushner 1997 and kunert martin 2000 this generalization places the method proposed by bailey druilhet 2004 into kushner s context the optimal designs obtained are not binary as in kunert martin 2000 we also propose efficient designs generated by only one sequence