adaptive anisotropic wavelet collocation method on general curvilinear coordinate systems a new general framework for an adaptive anisotropic wavelet collocation method a awcm for the solution of partial differential equations is developed this proposed framework addresses two major shortcomings of existing wavelet based adaptive numerical methodologies namely the reliance on a rectangular domain and the curse of anisotropy i e drastic over resolution of sheet and filament like features arising from the inability of the wavelet refinement mechanism to distinguish highly correlated directional information in the solution the a awcm addresses both of these challenges by incorporating coordinate transforms into the adaptive wavelet collocation method for the solution of pdes the resulting integrated framework leverages the advantages of both the curvilinear anisotropic meshes and wavelet based adaptive refinement in a complimentary fashion resulting in greatly reduced cost of resolution for anisotropic features the proposed adaptive anisotropic wavelet collocation method retains the a priori error control of the solution and fully automated mesh refinement while offering new abilities through the flexible mesh geometry including body fitting the new a awcm is demonstrated for a variety of cases including parabolic diffusion acoustic scattering and unsteady external flow

pores resolving simulation of darcy flows a theoretical formulation and corresponding numerical solutions are presented for microscopic fluid flows in porous media with the domain sufficiently large to reproduce integral darcy scale effects pore space geometry and topology influence flow through media but the difficulty of observing the configurations of real pore spaces limits understanding of their effects a rigorous direct numerical simulation dns of percolating flows is a formidable task due to intricacies of internal boundaries of the pore space representing the grain size distribution by means of repelling body forces in the equations governing fluid motion greatly simplifies computational efforts an accurate representation of pore scale geometry requires that within the solid the repelling forces attenuate flow to stagnation in a short time compared to the characteristic time scale of the pore scale flow in the computational model this is achieved by adopting an implicit immersed boundary method with the attenuation time scale smaller than the time step of an explicit fluid model a series of numerical simulations of the flow through randomly generated media of different porosities show that computational experiments can be equivalent to physical experiments with the added advantage of nearly complete observability besides obtaining macroscopic measures of permeability and tortuosity numerical experiments can shed light on the effect of the pore space structure on bulk properties of darcy scale flows

krylov methods for the incompressible navier stokes equations methods are presented for time evolution steady state solving and linear stability analysis for the incompressible navier stokes equations at low to moderate reynolds numbers the methods use krylov subspaces constructed by the arnoldi process from actions of the explicit navier stokes right hand side and of its jacobian without inversion of the viscous operator time evolution is performed by a nonlinear extension of the method of exponential propagation steady states are calculated by inexact krylov newton iteration using orthores and gmres linear stability analysis is carried out using an implicitly restarted arnoldi process with implicit polynomial filters a detailed implementation is described for a pseudospectral calculation of the stability of taylor vortices with respect to wavy vortices in the couette taylor problem 9 1994 academic press inc

symmetry reduction for nonlinear relativistically invariant equations symmetry reduction is studied for the relativistically invariant scalar partial differential equation h u u 2 u 0 in n 1 dimensional minkowski space m n 1 the introduction of k symmetry variables 1 k as invariants of a subgroup g of the poincare group p n 1 having generic orbits of codimension k n in m n 1 reduces the equation to a pde in k variables all codimension 1 symmetry variables in m n 1 n arbitrary reducing the equation studied to an ode are found as well as all codimension 2 and 3 variables for the low dimensional cases n 2 3 the type of equation studied includes many cases of physical interest in particular nonlinear klein gordon equations such as the sine gordon equation and hamilton jacobi equations

modeling a no slip flow boundary with an external force field abstract a novel technique related to peskin s immersed boundary approach is used to introduce solid surfaces into a simulated flow field the navier stokes equations permit the presence of an externally imposed body force that may vary in space and time forces are chosen to lie along a desired surface and to have a magnitude and direction opposing the local flow such that the flow is brought to rest on an element of the surface for unsteady viscous flow the direct calculation of the needed force is facilitated by a feedback scheme in which the velocity is used to iteratively determine the desired value in particular we determine the surface body force from the relation f x 5 t t 0 u x 5 t dt u x 5 t for surface points x 5 velocity u time t and negative constants and examples are presented which include 2d flow around cylinders 3d turbulent channel flow where one boundary is simulated with a force field and turbulent channel flow over a riblet covered surface while the new method may be applied to complex geometries on a non cartesian mesh we have chosen to use a simple cartesian grid all simulations are done with a spectral code in a single computational domain without any mapping of the mesh

parallel adaptive wavelet collocation method for pdes a parallel adaptive wavelet collocation method for solving a large class of partial differential equations is presented the parallelization is achieved by developing an asynchronous parallel wavelet transform which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution the data are stored using tree like structure with tree roots starting at a priori defined level of resolution both static and dynamic domain partitioning approaches are developed for the dynamic domain partitioning trees are considered to be the minimum quanta of data to be migrated between the processes this allows fully automated and efficient handling of non simply connected partitioning of a computational domain dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process the parallel efficiency of the approach is discussed based on parallel adaptive wavelet based coherent vortex simulations of homogeneous turbulence with linear forcing at effective non adaptive resolutions up to 20483 using as many as 2048 cpu cores

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

state feedback impulse elimination of linear time varying singular systems abstract linear time varying singular systems e t x a t x b t u are treated a necessary and sufficient condition for the existence of linear state feedback to eliminate impulsive behavior is derived the condition obtained is a natural extension of existing time invariant theory

derivative and proportional state feedback for linear descriptor systems with variable coefficients abstract we study linear descriptor systems with rectangular variable coefficient matrices using local and global equivalence transformations we introduce normal and condensed forms and get sets of characteristic quantities these quantities allow us to decide whether a linear descriptor system with variable coefficients is regularizable by derivative and or proportional state feedback or not regularizable by feedback means for us that there exists a feedback which makes the closed loop system uniquely solvable for every consistent initial vector

a penalization method to take into account obstacles in incompressible viscous flows from the navier stokes brinkman model a penalization method has been derived by several authors to compute incompressible navier stokes equations around obstacles in this paper convergence theorems and error estimates are derived for two kinds of penalization the first one corresponds to l 2 penalization inducing a darcy equation in the solid body the second one corresponds to a h 1 penalization and induces a brinkman equation in the body numerical tests are performed to confirm the efficiency and accuracy of the method

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

adaptive haar wavelets for the angular discretisation of spectral wave models a new framework for applying anisotropic angular adaptivity in spectral wave modelling is presented the angular dimension of the action balance equation is discretised with the use of haar wavelets hierarchical piecewise constant basis functions with compact support and an adaptive methodology for anisotropically adjusting the resolution of the angular mesh is proposed this work allows a reduction of computational effort in spectral wave modelling through a reduction in the degrees of freedom required for a given accuracy with an automated procedure and minimal cost

an immersed boundary method with formal second order accuracy and reduced numerical viscosity a formally second order accurate immersed boundary method is presented and tested in this paper we apply this new scheme to simulate the flow past a circular cylinder and study the effect of numerical viscosity on the accuracy of the computation by comparing the numerical results with those of a first order method the numerical evidence shows that the new scheme has less numerical viscosity and is therefore a better choice for the simulation of high reynolds number flows with immersed boundaries

penalization modeling of a limiter in the tokamak edge plasma an original penalization method is applied to model the interaction of magnetically confined plasma with limiter in the frame of a minimal transport model for ionic density and parallel momentum the limiter is considered as a pure particle sink for the plasma and consequently the density and the momentum are enforced to be zero inside comparisons of the numerical results with one dimensional analytical solutions show a very good agreement in particular the penalization scheme followed in this paper tends to ensure an almost sonic plasma condition at the plasma obstacle interface bohm like criterion with relatively weak dependence on the target mach number profile within the obstacle the new system being solved in a periodic obstacle free domain an efficient pseudo spectral algorithm based on a fast fourier transform is also proposed and associated with an exponential filtering of the unphysical oscillations due to gibbs phenomenon finally the efficiency of the method is illustrated by investigating the flow spreading from the plasma core to the scrape off layer at the wall in a two dimensional system with one then two neighboring limiters

an adaptive wavelet collocation method for solving optimal control of elliptic variational inequalities of the obstacle type abstract this paper presents a fast computational technique based on the wavelet collocation method for the numerical solution of an optimal control problem governed by elliptic variational inequalities of obstacle type in this problem the solution divides the domain into contact and noncontact sets the boundary between the contact and noncontact sets is a free boundary which is not known a priori and the solution is not smooth on it accordingly a very fine grid is needed in order to obtain a solution with a reasonable accuracy in this paper our aim is to propose an adaptive scheme in order to generate an appropriate and economic irregular dyadic mesh for finding the optimal control and state functions the irregular mesh will be generated such that its density around the free boundary is higher than in other places and high resolution computations are focused on these zones to this aim we use an adaptive wavelet collocation method and take advantage of the fast wavelet transform of compact supported interpolating wavelets to develop a multi level algorithm which generates an adaptive computational grid using this adaptive grid takes less cpu time than using a full regular mesh at each step of the algorithm the active set method is used for solving the optimality system of the obstacle problem on the adapted mesh finally the numerical examples are presented to show the validity and efficiency of the technique

convergence of a brinkman type penalization for compressible fluid flows abstract we show convergence of a brinkman type penalization of the compressible navier stokes equation in particular the existence of weak solutions for the system in domains with boundaries varying in time is established

adaptive wavelet collocation method on the shallow water model this paper presents an integrated approach for modeling several ocean test problems on adaptive grids using novel boundary techniques the adaptive wavelet collocation method solves the governing equations on temporally and spatially varying meshes which allows higher effective resolution to be obtained with less computational cost it is a general method for the solving a large class of partial differential equations but is applied to the shallow water equations here in addition to developing wavelet based computational models this work also uses an extension of the brinkman penalization method to represent irregular and non uniform continental boundaries this technique is used to enforce no slip boundary conditions through the addition of a term to the field equations when coupled with the adaptive wavelet collocation method the flow near the boundary can be well resolved it is especially useful for simulations of boundary currents and tsunamis where flow and the boundary is important thus those are the test cases presented here

second generation wavelet collocation method for the solution of partial differential equations an adaptive numerical method for solving partial differential equations is developed the method is based on the whole new class of second generation wavelets wavelet decomposition is used for grid adaptation and interpolation while a new o n hierarchical finite difference scheme which takes advantage of wavelet multilevel decomposition is used for derivative calculations the treatment of nonlinear terms and general boundary conditions is a straightforward task due to the collocation nature of the algorithm in this paper we demonstrate the algorithm for one particular choice of second generation wavelets namely lifted interpolating wavelets on an interval with uniform regular sampling the main advantage of using second generation wavelets is that wavelets can be custom designed for complex domains and irregular sampling thus the strength of the new method is that it can be easily extended to the whole class of second generation wavelets leaving the freedom and flexibility to choose the wavelet basis depending on the application

robust controllability for linear uncertain descriptor systems in this paper under assumptions that the linear nominal descriptor system is regular and controllable some sufficient conditions are proposed to preserve the assumed properties when both structured elemental and unstructured norm bounded parameter uncertainties are added into the nominal descriptor system besides another sufficient conditions are also presented to preserve the assumed properties for a class of linear descriptor systems having structured uncertainties in the structure information matrix as well as having both structured and unstructured parameter uncertainties in the system matrix and the input matrix simultaneously the corresponding results for the dual observability robustness problems are straightforward extensions three numerical examples are given to illustrate the applications of the proposed sufficient conditions and it is shown that the proposed sufficient conditions could be less conservative than the existing ones reported recently in the literature

time domain solution to descriptor variable systems the time domain solution to the fast subsystem of the descriptor variable system of the form ex spl dot ax bu with e singular is given by laplace inverse transformation a new and significant feature of the solution is that it contains impulse terms excited by the values of sufficiently smooth input u and its derivatives at the initial time point based on the solution the notions of consistent initial conditions classical solutions and impulse free solutions are discussed perfectly the impulse controllability is discussed also which admits the same interpretation as the controllability at infinity in frequency domain

exact solutions for the nonlinear klein gordon and liouville equations in four dimensional euclidean space a systematic method for constructing particular solutions of the nonlinear klein gordon and liouville equations in four spatial dimensions is developed the method of solution presented here first consists of reducing nonlinear partial differential equations to ordinary differential equations ode s by introducing symmetry variables and then seeking exact solutions for more tractable ode s various exact solutions are presented in which new solutions with nonspherical symmetries are included furthermore the exact method is applied to the above equations in general n spatial dimensions among them a conformally invariant nonlinear klein gordon equation is particularly interesting from the viewpoint of field theories the exact solutions for these equations are generalizations of those for the corresponding equations in four spatial dimensions

classical and generalized solutions of time dependent linear differential algebraic equations abstract a coordinate free reduction procedure is developed for linear time dependent differential algebraic equations that transforms their solutions into solutions of smaller systems of ordinary differential equations the procedure applies to classical as well as distribution solutions in the case of analytic coefficients the hypotheses required for the reduction not only are necessary for the validity of the existence and uniqueness results but even allow for the presence of singularities straightforward extensions including undetermined systems and systems with nonanalytic coefficients are also discussed

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

numerical simulation of a cylinder in uniform flow in this study a virtual boundary technique is applied to the numerical simulation of stationary and moving cylinders in uniform flow this approach readily allows the imposition of a no slip boundary within the flow field by a feedback forcing term added to the momentum equations in the present work this technique is used with a high order finite difference method effectively eliminating spurious oscillations caused by the feedback forcing when used with spectrally discretized flow solvers very good agreement is found between the present calculations and previous computational and experimental results for steady and time dependent flow at low reynolds numbers

controllability and observability of linear time varying singular systems controllability and observability of analytically solvable linear time varying singular systems are considered our analysis includes the possible impulsive zero input response based on the definitions of controllability and observability naturally extended from the ones adopted in the time invariant setting sufficient and necessary conditions for these two properties are derived furthermore according to the specific definitions of these concepts used here the authors show that the dual relationship between controllability and observability does not hold

impulse analysis of linear time varying singular systems impulsive part of solution to initial value problem of linear time varying singular systems is given explicitly impulse observability and impulse controllability for the systems are redefined

a ghost cell immersed boundary method for flow in complex geometry an efficient ghost cell immersed boundary method gcibm for simulating turbulent flows in complex geometries is presented a boundary condition is enforced through a ghost cell method the reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second order accuracy of the base solver both dirichlet and neumann boundary conditions can be treated the current ghost cell treatment is both suitable for staggered and non staggered cartesian grids the accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface numerical results are compared with experimental data and boundary fitted grid results the method is further extended to an existing ocean model mitgcm to simulate geophysical flow over a three dimensional bump the method is easily implemented as evidenced by our use of several existing codes

an implicit boundary approach for viscous compressible high reynolds flows using a hybrid remeshed particle hydrodynamics method abstract we present an implicit boundary particle method with background mesh adaptation we use a brinkman penalisation to represent the boundary of the domain and a remeshed particle method to simulate viscous flow with high reynolds numbers a penalty term is added to the navier stokes equations to impose the boundary conditions the boundary conditions are enforced to a specific precision with no need to modify the numerical method or change the grid achieving an implicit approach for flow around complex boundaries geometries simulation the main idea of the brinkman penalisation method is to model the solid obstacle as a porous medium the governing equations for the compressible fluid and penalised navier stokes for the porous medium are solved simultaneously without need for interface conditions the accuracy of the method is tested for a number of benchmark problems starting with simple cases such as a periodic laminar flow in a channel poiseuille flow to more complex problems such as the lid driven cavity with high reynolds numbers the reflection and propagation of a compressible shock wave and finally swirling flow in a model two stroke diesel engine the remeshed particle mesh method coupled with brinkman penalisation provides a good quality simulation and the results are in agreement with analytical or reference solutions

wronskians geometry and some general solutions to the nonlinear liouville like pde s the formal properties of n dimensional wronskians and their geometric interpretation enable one to construct explicit analytic solutions to some nonlinear partial differential equations pde s that generalize the liouville equation xy e2 the studied pde s are a lmf const b lmf g lmg f and c lm lmf const where lm is the nonlinear differential operation lmf det kx lyf with k l 0 1 m some nontrivial formal properties of the composition of the lm s are established

an adaptive multilevel wavelet collocation method for elliptic problems an adaptive multilevel wavelet collocation method for solving multi dimensional elliptic problems with localized structures is described the method is based on multi dimensional second generation wavelets and is an extension of the dynamically adaptive second generation wavelet collocation method for evolution problems int j comp fluid dyn 17 2003 151 wavelet decomposition is used for grid adaptation and interpolation while a hierarchical finite difference scheme which takes advantage of wavelet multilevel decomposition is used for derivative calculations the multilevel structure of the wavelet approximation provides a natural way to obtain the solution on a near optimal grid in order to accelerate the convergence of the solver an iterative procedure analogous to the multigrid algorithm is developed the overall computational complexity of the solver is o n where n is the number of adapted grid points the accuracy and computational efficiency of the method are demonstrated for the solution of two and three dimensional elliptic test problems

a brinkman penalization method for compressible flows in complex geometries to simulate flows around solid obstacles of complex geometries various immersed boundary methods had been developed their main advantage is the efficient implementation for stationary or moving solid boundaries of arbitrary complexity on fixed non body conformal cartesian grids the brinkman penalization method was proposed for incompressible viscous flows by penalizing the momentum equations its main idea is to model solid obstacles as porous media with porosity f and viscous permeability approaching zero it has the pronounced advantages of mathematical proof of error bound strong convergence and ease of numerical implementation with the volume penalization technique in this paper it is extended to compressible flows the straightforward extension of penalizing momentum and energy equations using brinkman penalization with respective normalized viscous h and thermal h t permeabilities produces unsatisfactory results mostly due to nonphysical wave transmissions into obstacles resulting in considerable energy and mass losses in reflected waves the objective of this paper is to extend the brinkman penalization technique to compressible flows based on a physically sound mathematical model for compressible flows through porous media in addition to penalizing momentum and energy equations the continuity equation for porous media is considered inside obstacles in this model the penalized porous region acts as a high impedance medium resulting in negligible wave transmissions the asymptotic analysis reveals that the proposed brinkman penalization technique results in the amplitude and phase errors of order o email protected 1 2 and o h h t 1 email protected 3 4 when the boundary layer within the porous media is respectively resolved or unresolved the proposed method is tested using 1 and 2 d benchmark problems the results of direct numerical simulation are in excellent agreement with the analytical solutions the numerical simulations verify the accuracy and convergence rates

coherent vortex simulation of weakly compressible turbulent mixing layers using adaptive multiresolution methods an adaptive mulitresolution method based on a second order finite volume discretization is presented for solving the three dimensional compressible navier stokes equations in cartesian geometry the explicit time discretization is of second order and for flux evaluation a 2 4 mac cormack scheme is used coherent vortex simulations cvs are performed by decomposing the flow variables into coherent and incoherent contributions the coherent part is computed deterministically on a locally refined grid using the adaptive multiresolution method while the influence of the incoherent part is neglected to model turbulent dissipation the computational efficiency of this approach in terms of memory and cpu time compression is illustrated for turbulent mixing layers in the weakly compressible regime and for reynolds numbers based on the mixing layer thickness between 50 and 200 comparisons with direct numerical simulations allow to assess the precision and efficiency of cvs

finite time stability of linear time varying singular systems with impulsive effects in this paper we introduce a new concept of finite time stability of linear time varying singular systems with impulses at fixed times and present new results for the above mentioned class of system in the form of sufficient conditions a sufficient condition is given in terms of matrix inequalities which gives the opportunity of fitting the finite time control problem in the general framework via impulsive control a numerical example is presented to illustrate the efficiency of the proposed result

dns of buoyancy dominated turbulent flows on a bluff body using the immersed boundary method a novel immersed boundary ib method has been developed for simulating multi material heat transfer problem a cylinder in a channel heated from below with mixed convection the method is based on a second order velocity scalar reconstruction near the ib a novel algorithm has been developed for the ib method to handle conjugate heat transfer the fluid solid interface is constructed as a collection of disjoint faces of control volumes associated to different material zones coupling conditions for the material zones have been developed such that continuity and conservation of the scalar flux are satisfied by a second order interpolation predictions of the local nusselt number on the cylinder surface show good agreement with the experimental data the effect of the boussinesq approximation on this problem was also investigated comparison with the variable density formulation suggests that in spite of a small thermal expansion coefficient of water the variable density formulation in a transitional flow with mixed convection is preferable

time dependent linear daes with discontinuous inputs existence and uniqueness results are proved for initial value problems associated with linear time varying differential algebraic equations the right hand sides are chosen in a space of distributions allowing for solutions exhibiting discontinuities as well as impulses this approach also provides a satisfactory answer to the problem of inconsistent initial conditions of crucial importance for physical applications furthermore our theoretical results yield an efficient numerical procedure for the calculation of the jump and impulse of a solution at a point of discontinuity numerical examples are given

a characteristic based volume penalization method for general evolution problems applied to compressible viscous flows in order to introduce solid obstacles into flows several different methods are used including volume penalization methods which prescribe appropriate boundary conditions by applying local forcing to the constitutive equations one well known method is brinkman penalization which models solid obstacles as porous media while it has been adapted for compressible incompressible viscous and inviscid flows it is limited in the types of boundary conditions that it imposes as are most volume penalization methods typically approaches are limited to dirichlet boundary conditions in this paper brinkman penalization is extended for generalized neumann and robin boundary conditions by introducing hyperbolic penalization terms with characteristics pointing inward on solid obstacles this characteristic based volume penalization cbvp method is a comprehensive approach to conditions on immersed boundaries providing for homogeneous and inhomogeneous dirichlet neumann and robin boundary conditions on hyperbolic and parabolic equations this cbvp method can be used to impose boundary conditions for both integrated and non integrated variables in a systematic manner that parallels the prescription of exact boundary conditions furthermore the method does not depend upon a physical model as with porous media approach for brinkman penalization and is therefore flexible for various physical regimes and general evolutionary equations here the method is applied to scalar diffusion and to direct numerical simulation of compressible viscous flows with the navier stokes equations both homogeneous and inhomogeneous neumann boundary conditions are demonstrated through external flow around an adiabatic and heated cylinder theoretical and numerical examination shows that the error from penalized neumann and robin boundary conditions can be rigorously controlled through an a priori penalization parameter h the error on a transient boundary is found to converge as o h which is more favorable than the error convergence of the already established dirichlet boundary condition

technical communique impulse observability and impulse controllability of linear time varying singular systems impulse controllability and impulse observability of linear time varying singular systems in a standard canonical form are examined we focus on the fast subsystems with constant rank n matrices sufficient and necessary conditions are derived and presented directly in terms of system parameters conditions obtained for these two properties are algebraically dual to each other

isogroups and exact solutions for some klein gordon and liouville type equations in n dimensional euclidean space using the elementary symmetric functions of n euclidean coordinates xn as symmetry variables and the isovector approach the generalized forms of nonlinear klein gordon and liouville equations in n dimensional euclidean space are analyzed herein the construction of the components of the associated isovector field via transport property under lie derivative leads to orbital equations whose solutions yield invariant groups of transformations these invariant groups reduce the equations under consideration to nonlinear ordinary differential equations odes involving arbitrary functions of the new dependent and independent variables finally exact solutions of these resulting odes are tabulated for different forms of these arbitrary functions beside recovering the available results for particular forms of the said arbitrary functions involved in the ordinary differential equations some new exact solutions are reported

regularization of linear descriptor systems with variable coefficients we study linear descriptor control systems with rectangular variable coefficient matrices we introduce condensed forms for such systems under equivalence transformations and use these forms to detect whether the system can be transformed to a uniquely solvable closed loop system via state or derivative feedback we show that under some mild assumptions every such system consists of an underlying square subsystem that behaves essentially like a standard state space system plus some solution components that are constrained to be zero

flusi a novel parallel simulation tool for flapping insect flight using a fourier method with volume penalization we introduce flusi a fully parallel open source software package for pseudospectral simulations of three dimensional flapping flight in viscous flows it is freely available for noncommercial use from github https github com pseudospectators flusi the computational framework runs on high performance computers with distributed memory architectures the discretization of the three dimensional incompressible navier stokes equations is based on a fourier pseudospectral method with adaptive time stepping the complex time varying geometry of insects with rigid flapping wings is handled using the volume penalization method the modules characterizing the insect geometry flight mechanics and wing kinematics are described validation tests for different benchmarks illustrate the efficiency and precision of the approach finally computations for a model insect in the turbulent regime demonstrate the versatility of the software

an adaptive wavelet collocation method for fluid structure interaction at high reynolds numbers two mathematical approaches are combined to calculate high rey nolds number incompressible fluid structure interaction a wavelet method to dynamically adapt the computational grid to flow intermittency and obstacle motion and brinkman penalization to enforce solid boundaries of arbitrary complexity we also implement a wavelet based multilevel solver for the poisson problem for the pressure at each time step the method is applied to two dimensional flow around fixed and moving cylinders for reynolds numbers in the range 3 times 10 1 le re le 10 5 the compression ratios of up to 1000 are achieved for the first time it is demonstrated in actual dynamic simulations that the compression scales like re 1 2 over five orders of magnitude while computational complexity scales like re this represents a significant improvement over the classical complexity estimate of re 9 4 for two dimensional turbulence

prediction of wall pressure fluctuation in turbulent flows with an immersed boundary method the objective of this paper is to assess the accuracy and efficiency of the immersed boundary ib method to predict the wall pressure fluctuations in turbulent flows where the flow dynamics in the near wall region is fundamental to correctly predict the overall flow the present approach achieves sufficient accuracy at the immersed boundary and overcomes deficiencies in previous ib methods by introducing additional constraints a compatibility for the interpolated velocity boundary condition related to mass conservation and the formal decoupling of the pressure on this surfaces the immersed boundary approximated domain method ib adm developed in the present study satisfies these conditions with an inexpensive computational overhead the ib adm correctly predicts the near wall velocity pressure and scalar fields in several example problems including flows around a very thin solid object for which incorrect results were obtained with previous ib methods in order to have sufficient near wall mesh resolution for les and dns computations the present approach uses local mesh refinement the present method has been also successfully applied to computation of the wall pressure space time correlation in dns of turbulent channel flow on grids not aligned with the boundaries when applied to a turbulent flow around an airfoil the computed flow statistics the mean rms flow field and power spectra of the wall pressure are in good agreement with experiment

the output nulling space projected dynamics and system decomposition for linear time varying singular systems a decomposition of a given linear time varying singular control system is developed by defining the output nulling space with respect to a given output structure relevant subspaces and the dynamics on them are described by computable projection operators obtained from information in the system s derivative array the relevant projectors are generated as solutions of a homogeneous linear matrix differential equation an algorithm for obtaining the system decomposition is outlined in a pointwise manner

stochastic generation of explicit pore structures by thresholding gaussian random fields abstract we provide a description and computational investigation of an efficient method to stochastically generate realistic pore structures smolarkiewicz and winter introduced this specific method in pores resolving simulation of darcy flows smolarkiewicz and winter 2010 1 without giving a complete formal description or analysis of the method or indicating how to control the parameterization of the ensemble we address both issues in this paper the method consists of two steps first a realization of a correlated gaussian field or topography is produced by convolving a prescribed kernel with an initial field of independent identically distributed random variables the intrinsic length scales of the kernel determine the correlation structure of the topography next a sample pore space is generated by applying a level threshold to the gaussian field realization points are assigned to the void phase or the solid phase depending on whether the topography over them is above or below the threshold hence the topology and geometry of the pore space depend on the form of the kernel and the level threshold manipulating these two user prescribed quantities allows good control of pore space observables in particular the minkowski functionals extensions of the method to generate media with multiple pore structures and preferential flow directions are also discussed to demonstrate its usefulness the method is used to generate a pore space with physical and hydrological properties similar to a sample of berea sandstone

backlund generated solutions of liouville s equation and their graphical representations in three spatial dimensions the backlund bianchi method is employed to generate in three spatial dimensions the following multiple solutions of liouville s equation 2 exp the three wave interaction function 3 and the five wave interaction function 5 it is verified numerically that 3 satisfies liouville s equation to an accuracy of one part in 1014 while 5 satisfies it to one part in 106 the construction of 5 is conditional upon solving ten nonlinear constraint equations we analyze the complicated structures of 3 and 5 with the help of a three dimensional plotting routine it is found that 3 is surprisingly enough only characterized by a single ring singularity while 5 exhibits three ring singularities it is speculated that the function tanh 3 represents a ring soliton whose shape appears to be preserved in the nonlinear superposition of similar ring solitons the derivation of liouville s solutions 3 and 5 is intimately connected with the auxiliary functions 2 and 4 which solve laplace s equation the latter are also derived and plotted in the paper