finite element solution of compressible viscous flows using conservative variables abstract a finite element method for solving the compressible navier stokes equations is presented these equations are solved in conservation form and using conservative variables appropriate finite element approximations are discussed when a galerkin variational formulation is used for high speed flows the formulation is stabilized using the stream line upwind petrov galerkin method for which we propose an analytical expression for the matrix a new discontinuity capturing operator is also proposed to accurately solve flow problems exhibiting sharp gradients the non linear systems of equations arising from the discretization are solved using an iterative strategy based on the generalized minimal residual gmres algorithm numerical results for transonic and supersonic flows are presented that demonstrate the effectiveness of the proposed finite element method

a fast method for solving the heat equation by layer potentials boundary integral formulations of the heat equation involve time convolutions in addition to surface potentials if m is the number of time steps and n is the number of degrees of freedom of the spatial discretization then the direct computation of a heat potential involves order n2m2 operations this article describes a fast method to compute three dimensional heat potentials which is based on chebyshev interpolation of the heat kernel in both space and time the computational complexity is order p4q2nm operations where p and q are the orders of the polynomial approximation in space and time

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

a comparative study of different sets of variables for solving compressible and incompressible flows a globally conservative galerkin least squares formulation which attains correct shock structure is developed for any choice of variables only the choice of entropy variables satisfies exactly the discrete clausius duhem inequality without any dissipative mechanisms whereas for the rest of the variables artificial diffusion is required to guarantee entropy production the limit of the formulation is well defined for entropy variables and the primitive variables p u t leading to conservative incompressible formulations the approach is stable for any continuous interpolations both for compressible and incompressible flows a comparative study of different variables is performed indicating that entropy variables and the primitive variables p u t possess the most attributes for practical problem solving

a fast galerkin method for parabolic space time boundary integral equations an efficient scheme for solving boundary integral equations of the heat equation based on the galerkin method is introduced the parabolic fast multipole method pfmm is applied to accelerate the evaluation of the thermal layer potentials in order to remain attractive for a wide range of applications a key issue is to ensure efficiency for a big variety of temporal to spatial mesh ratios within the parabolic galerkin fmm pgfmm it turns out that the temporal nearfield can become very costly to that end a modified fast gauss transform fgt is developed the complexity and convergence behavior of the method are analyzed and numerically investigated on a range of model problems the results demonstrate that the complexity is nearly optimal in the number of discretization parameters while the convergence rate of the galerkin method is preserved

erratum to existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients by combining the theory of the exponential dichotomy and liapunov function we study the existence and attractivity of almost periodic solutions for cellular neural networks cnns with distributed delays and variable coefficientsdx idt b i t x i t j 1 na i j t f j x j t j 1 nb i j t f j m j 0 k i j u x j t u du i i t we obtain some sufficient conditions to ensure that for the networks there exists a unique almost periodic solution and all its solutions converge to such an almost periodic solution an example is given to illustrate that the conditions of our results are feasible

an unstructured finite elements method for solving the compressible rans equations and the spalart allmaras turbulence model this paper deals with a stabilized finite element method for solving the compressible navier stokes equations combined with the spalart allmaras turbulence model the aim is to assess the ability of this formulation to solve high reynolds number turbulent flows over anisotropic meshes this formulation lies in the framework of the stream line upwind petrove galerkin method we propose a simple and efficient formulation for the stabilization matrix and develop a shock capturing operator numerical tests on the 3d boundary layer over a flat plate and on the onera m6 wing show the stability and robustness of the proposed method

stability in asymmetric hopfield nets with transmission delays sufficient conditions are derived for the delay independent stability of the equilibria in hopfield s graded response networks of the type dxi t dt bixi t nj 1aijfj jxj t ij fi t i 1 2 n when the external inputs fi are held temporally uniform a generalization to continuously distributed delays is briefly indicated several illustrative examples are numerically simulated and the results of simulations are graphically displayed

bubble stabilization of finite element methods for the linearized incompressible navier stokes equations abstract in this paper we discuss the stabilization via bubble functions of a finite element method for stationary linearized incompressible navier stokes equations it is shown that residual free bubbles can reproduce supg

global exponential stability in dcnns with distributed delays and unbounded activations we study delayed cellular neural networks dcnns whose state variables are governed by nonlinear integrodifferential differential equations with delays distributed continuously over unbounded intervals the networks are designed in such a way that the connection weight matrices are not necessarily symmetric and the activation functions are globally lipschitzian and they are not necessarily bounded differentiable and monotonically increasing by applying the inequality pa p 1b p 1 a p b p where p denotes a positive integer and a b denote nonnegative real numbers and constructing an appropriate form of lyapunov functionals we obtain a set of delay independent and easily verifiable sufficient conditions under which the network has a unique equilibrium which is globally exponentially stable a few examples added with computer simulations are given to support our results

multistability and multiperiodicity of delayed cohen grossberg neural networks with a general class of activation functions abstract in this paper by using analysis approach and decomposition of state space the multistability and multiperiodicity issues are discussed for cohen grossberg neural networks cgnns with time varying delays and a general class of activation functions where the general class of activation functions consist of nondecreasing functions with saturation s including piecewise linear functions with two corner points and standard activation functions as its special case based on the cauchy convergence principle some sufficient conditions are obtained for checking the existence and uniqueness of equilibrium points of the n neuron cgnns it is shown that the n neuron cgnns can have 2n locally exponentially stable equilibrium points located in saturation regions also some conditions are derived for ascertaining equilibrium points to be locally exponentially stable or globally exponentially attractive and to be located in any designated region as an extension of multistability some similar results are presented for ascertaining multiple periodic orbits when external inputs of the n neuron cgnns are periodic finally three examples are given to illustrate the effectiveness of the obtained results

incompressible flow past a circular cylinder dependence of the computed flow field on the location of the lateral boundaries the influence of the location of the lateral boundaries on 2d computation of unsteady incompressible flow past a circular cylinder is investigated the case of reynolds number 100 is used as a benchmark and several quantities characterizing the unsteady flow are obtained for a range of lateral boundary locations the computations are performed with two distinct finite element formulations space time velocity pressure formulation and velocity pressure stress formulation we conclude that the distance between the cylinder and the lateral boundaries can have a significant effect on the strouhal number and other flow quantities the minimum distance at which this influence vanishes has been found to be larger than what is commonly assumed

boundary element formulations for the numerical solution of two dimensional diffusion problems with variable coefficients this paper presents new formulations of the radial integration boundary integral equation ribie and the radial integration boundary integro differential equation ribide methods for the numerical solution of two dimensional diffusion problems with variable coefficients the methods use either a specially constructed parametrix levi function or the standard fundamental solution for the laplace equation to reduce the boundary value problem bvp to a boundary domain integral equation bdie or boundary domain integro differential equation bdide the radial integration method rim is then employed to convert the domain integrals arising in both bdie and bdide methods into equivalent boundary integrals the resulting formulations lead to pure boundary integral and integro differential equations with no domain integrals furthermore a subdomain decomposition technique sdbdie is proposed which leads to a sparse system of linear equations thus avoiding the need to calculate a large number of domain integrals numerical examples are presented for several simple problems for which exact solutions are available to demonstrate the efficiency of the proposed approaches

theoretical aspects of the application of convolution quadrature to scattering of acoustic waves in this paper we address several theoretical questions related to the numerical approximation of the scattering of acoustic waves in two or three dimensions by penetrable non homogeneous obstacles using convolution quadrature cq techniques for the time variable and coupled boundary element method finite element method for the space variable the applicability of cq to waves requires polynomial type bounds for operators related to the operator s 2 in the right half complex plane we propose a new systematic way of dealing with this problem both at the continuous and semidiscrete in space cases we apply the technique to three different situations scattering by a group of sound soft and hard obstacles by homogeneous and non homogeneous obstacles

supg finite element computation of compressible flows with the entropy and conservation variables formulations abstract supg stabilized finite element formulations of compressible euler equations based on the conservation and entropy variables are investigated and compared the formulation based on the conservation variables consists of the formulation introduced by tezduyar and hughes plus a shock capturing term the formulation based on the entropy variables is the same as the one by hughes franca and mallet which has a shock capturing term built in these formulations are tested on several subsonic transonic and supersonic compressible flow problems it is shown that the stabilized formulation based on the conservation variables gives solutions which are just as good as those obtained with the entropy variables furthermore the solutions obtained using the two formulations are very close and in some cases almost indistinguishable consequently it can be deduced that the relative merits of these two formulations will continue to remain under debate

time discretization of parabolic boundary integral equations in time dependent boundary integral equations a boundary element method in space can be coupled with a different type of discretization in time for the latter a procedure based on linear multistep methods is proposed which is applicable whenever the laplace transform of the fundamental solution is known the stability properties of the method are obtained from those of the underlying multistep method in the absence of a space discretization the numerical solution given by the proposed method is identical to that of a semi discretization in time of the partial differential equation by the underlying multistep method the theory is presented for the single layer potential equation of the heat equation convergence estimates which are pointwise in time and expressed in terms of the boundary data are obtained for full discretizations using galerkin or collocation boundary element methods in space numerical examples are included

rapid solution of the wave equation in unbounded domains in this paper we propose and analyze a new fast method for the numerical solution of time domain boundary integral formulations of the wave equation we employ lubich s convolution quadrature method for the time discretization and a galerkin boundary element method for the spatial discretization the coefficient matrix of the arising system of linear equations is a triangular block toeplitz matrix possible choices for solving the linear system arising from the above discretization include the use of fast fourier transform fft techniques and the use of data sparse approximations by using fft techniques the computational complexity can be reduced substantially while the storage cost remains unchanged and is typically high using data sparse approximations the gain is reversed i e the computational cost is approximately unchanged while the storage cost is substantially reduced the method proposed in this paper combines the advantages of these two approaches first the discrete convolution related to the block toeplitz system is transformed into the discrete fourier image thereby arriving at a decoupled system of discretized helmholtz equations with complex wave numbers a fast data sparse e g fast multipole or panel clustering method can then be applied to the transformed system additionally significant savings can be achieved if the boundary data are smooth and time limited in this case the right hand sides of many of the helmholtz problems are almost zero and hence can be disregarded finally the proposed method is inherently parallel we analyze the stability and convergence of these methods thereby deriving the choice of parameters that preserves the convergence rates of the unperturbed convolution quadrature we also present numerical results which illustrate the predicted convergence behavior

stabilized finite element methods for the velocity pressure stress formulation of incompressible flows abstract formulated in terms of velocity pressure and the extra stress tensor the incompressible navier stokes equations are discretized by stabilized finite element methods the stabilized methods proposed are analyzed for a linear model and extended to the navier stokes equations the numerical tests performed confirm the good stability characteristics of the methods these methods are applicable to various combinations of interpolation functions including the simplest equal order linear and bilinear elements

convergence analyses of galerkin least squares methods for symmetric advective diffusive forms of the stokes and incompressible navier stokes equations abstract symmetric advective diffusive forms of the stokes and incompressible navier stokes equations are presented the galerkin least squares method for advective diffusive equations is used for both systems and is related to other stabilized methods previously studied the presentation reveals that the convergence analysis for advective diffusive equations as applied before to a linearized form of the compressible navier stokes equations carries over in a straightforward manner to the stokes problem and to a linearized form of the incompressible navier stokes equations

a straightforward structure to construct shape functions for variable p order meshes this paper describes a method for specifying variable p order meshes based on the topological hierarchy of mesh entities defining the finite elements a decomposition of p version mesh entity shape functions into a product of a function defined over the mesh entity and a blending function defined over the elements that the mesh entity bounds is presented the decomposed shape functions allow the effective construction of the shape functions and derivatives needed to construct element matrices for variable p enrichment

algebraic approximation of sub grid scales for the variational multiscale modeling of transport problems abstract variational multiscale vms finite element methods fems are robust for the development of general formulations for the solution of multiphysics and multiscale transport problems to obtain a tractable and computationally efficient model vms methods often rely on a residual based algebraic approximation of the sub grid scales small or unresolved features of the solution field not captured by the discretization using a so called intrinsic time scales matrix which depends on the problem s overall differential operator and represents the main model parameter a novel technique for approximating the intrinsic time scales matrix for generic transport problems in a relatively inexpensive manner e g does not rely on eigenvalue computations is presented the method is denoted transport equivalent scaling tes and is based on the monolithic casting of the transport problem as a system of transient advective diffusive reactive tadr equations and a subsequent scaling of the coefficient matrices such to preserve each type of transport flux an algebraic vms formulation incorporating the tes method is complemented with a discontinuity capturing dc approach and implemented within a fem solver for the solution of tadr problems the solution of the global discrete system is accomplished using a generalized alpha time stepper together with a globalized inexact newton krylov nonlinear solver the effectiveness of the tes formulation is verified with the simulation of benchmark incompressible compressible and magnetohydrodynamic flow problems the results demonstrate that the tes method seamlessly handles incompressible compressible flows in a unified manner e g without assessing the compressibility of the flow the convergence process using the tes approach and a more standard approximation for the intrinsic time scales as well as the effect of the dc approach are also investigated analysis of the intrinsic time scales for a one dimensional incompressible flow model reveals the similitudes and differences between the tes formulation and other conventional methods

pth moment stability analysis of stochastic recurrent neural networks with time varying delays this paper addresses in great detail the issue of pth moment exponential stability of stochastic recurrent neural networks with time varying delays with the help of the dini derivative of the expectation of v t x t along the solution x t of the model and the technique of halanay type inequality some novel sufficient conditions on pth moment exponential stability of the trivial solution has been established results of the development as presented in this paper are more general than those reported in some previously published papers an example is also given to illustrate that our results are correct and effectiveness

stability analysis of cohen grossberg neural networks without assuming boundedness and differentiability of the activation functions and any symmetry of interconnections we employ lyapunov functions to establish some sufficient conditions ensuring existence uniqueness global asymptotic stability and even global exponential stability of equilibria for the cohen grossberg neural networks with and without delays our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria and can be applied to neural networks including hopfield neural networks bidirectional association memory neural networks and cellular neural networks

scale separating operators for variational multiscale large eddy simulation of turbulent flows a general class of scale separating operators based on combined multigrid operators is proposed and analyzed in this work the operators of this class are designed for variational multiscale large eddy simulation using a finite volume or finite element method two representatives are compared to discrete smooth filters which are widely used in the traditional large eddy simulation literature the comparison shows that they are not only theoretically different but also yield considerable differences in the respective numerical results dynamic as well as constant coefficient based subgrid scale modeling is used within the multiscale environment all of the scale separating operators are implemented in a second order accurate energy conserving finite volume method and tested for the case of a turbulent channel flow one operator shows particularly remarkable results in the framework of the variational multiscale large eddy simulation that is profiles are obtained for velocity and kinetic energy which are considerably closer to the respective profiles from a direct numerical simulation than are the profiles resulting from the application of the other operators considered in the present study furthermore this particular operator proves to be very efficient with regard to the important aspect of computational cost that is a reduction in computing time ranging from about 25 up to about 150 compared to the other operators the introduction of a substantial amount of subgrid viscosity to the small scales particularly in the buffer layer of the channel appears to be crucial for the good results achieved with this method

stability analysis of markovian jumping stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotical stability analysis problem is considered for a class of markovian jumping stochastic cohen grossberg neural networks cgnns with mixed delays including discrete delays and distributed delays an alternative delay dependent stability analysis result is established based on the linear matrix inequality lmi technique which can easily be checked by utilizing the numerically efficient matlab lmi toolbox neither system transformation nor free weight matrix via newton leibniz formula is required two numerical examples are included to show the effectiveness of the result

global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays by employing the lyapunov krasovskii functional and linear matrix inequality lmi approach the problem of global asymptotical stability is studied for recurrent neural networks with both discrete time varying delays and distributed time varying delays some sufficient conditions are given for checking the global asymptotical stability of recurrent neural networks with mixed time varying delay the proposed lmi result is computationally efficient as it can be solved numerically using standard commercial software two examples are given to show the usefulness of the results

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100

a better consistency for low order stabilized finite element methods abstract the standard implementation of stabilized finite element methods with a piece wise function space of order lower than the highest derivative present in the partial differential equation often suffers from a weak consistency that can lead to reduced accuracy the popularity of these low order elements motivates the development of a new stabilization operator which globally reconstructs the derivatives not present in the local element function space this new method is seen to engender a stronger consistency leading to better convergence and improved accuracy applications to the navier stokes equations are given which illustrate the improvement at a negligible additional cost

global asymptotic stability of reaction diffusion cohen grossberg neural networks with continuously distributed delays this paper is concerned with the global asymptotic stability of a class of reaction diffusion cohen grossberg neural networks with continuously distributed delays under some suitable assumptions and using a matrix decomposition method we apply the linear matrix inequality lmi method to propose some new sufficient stability conditions for the reaction diffusion cohen grossberg neural networks with continuously distributed delays the obtained results are easy to check and improve upon the existing stability results some remarks are given to show the advantages of the obtained results over the previous results an example is also given to demonstrate the effectiveness of the obtained results

a finite element formulation of compressible flows using various sets of independent variables abstract this paper presents a finite element method for the simulation of compressible flows the navier stokes and euler equations are solved in the conservation form using various sets of independent variables a variational formulation is developed based upon a variant of the petrov galerkin method and uses a shock capturing operator an adaptive algorithm based on a particular residual norm is proposed several numerical examples are presented to demonstrate the performances of each set of variables in solving compressible high speed flows

segregated runge kutta time integration of convection stabilized mixed finite element schemes for wall unresolved les of incompressible flows in this work we develop a high performance numerical framework for the large eddy simulation les of incompressible flows the spatial discretization of the nonlinear system is carried out using mixed finite element fe schemes supplemented with symmetric projection stabilization of the convective term and a penalty term for the divergence constraint these additional terms introduced at the discrete level have been proved to act as implicit les models in order to perform meaningful wall unresolved simulations we consider a weak imposition of the boundary conditions using a nitsche s type scheme where the tangential component penalty term is designed to act as a wall law next segregated runge kutta srk schemes recently proposed by the authors for laminar flow problems are applied to the les simulation of turbulent flows by the introduction of a penalty term on the trace of the acceleration these methods exhibit excellent stability properties for both implicit and explicit treatment of the convective terms srk schemes are excellent for large scale simulations since they reduce the computational cost of the linear system solves by splitting velocity and pressure computations at the time integration level leading to two uncoupled systems the pressure system is a darcy type problem that can easily be preconditioned using a traditional block preconditioning scheme that only requires a poisson solver at the end only coercive systems have to be solved which can be effectively preconditioned by multilevel domain decomposition schemes which are both optimal and scalable the framework is applied to the taylor green and turbulent channel flow benchmarks in order to prove the accuracy of the convection stabilized mixed fes as les models and srk time integrators the scalability of the preconditioning techniques in space only has also been proven for one step of the srk scheme for the taylor green flow using uniform meshes moreover a turbulent flow around a naca profile is solved to show the applicability of the proposed algorithms for a realistic problem

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

convergence dynamics of stochastic cohen grossberg neural networks with unbounded distributed delays this paper addresses the issue of the convergence dynamics of stochastic cohen grossberg neural networks scgnns with white noise whose state variables are described by stochastic nonlinear integro differential equations with the help of lyapunov functional semi martingale theory and inequality techniques some novel sufficient conditions on pth moment exponential stability and almost sure exponential stability for scgnn are given furthermore as byproducts of our main results some sufficient conditions for checking stability of deterministic cgnns with unbounded distributed delays have been established especially even when the spectral radius of the coefficient matrix is greater than 1 in some cases our theory is also effective

hierarchical basis for stabilized finite element methods for compressible flows the quest for more accurate numerical simulations of the navier stokes equations has motivated the study of high order piecewise polynomial basis functions also known as k version finite element methods as a means to attain this accuracy in the most cost effective manner stabilized finite element methods e g streamline upwind petrov galerkin have been proven to attain optimal rates of convergence for any polynomial order basis as well as perform well on a variety of flows including turbulence applications we present a stabilized finite element formulation for fluid dynamics using mesh entity based hierarchical basis functions the implementation is shown to attain theoretical convergence results for the linear model problem as well as the navier stokes equations

a variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes application to vortex shedding the variational multiscale formulation of large eddy simulations developed by hughes and his co workers for incompressible turbulent flows is first extended to the case of compressible turbulent flows next a finite volume element discretization on tetrahedral meshes of this method is proposed this discretization features an economical procedure based on agglomeration for separating a priori the scales a corresponding projector for eliminating the small scales from the system of equations and an effective control of the numerical dissipation induced by upwinding the resulting les method is validated with the three dimensional numerical simulation of a low speed flow past a square cylinder at m 0 1 and re 22 000 and various comparisons with experimental data

runge kutta convolution quadrature for operators arising in wave propagation an error analysis of runge kutta convolution quadrature is presented for a class of non sectorial operators whose laplace transform satisfies besides the standard assumptions of analyticity in a half plane re s 0 and a polynomial bound operatorname o s mu 1 there the stronger polynomial bound operatorname o s mu 2 in convex sectors of the form operatorname arg s leq pi 2 theta for 0 the order of convergence of the runge kutta convolution quadrature is determined by 2 and the underlying runge kutta method but is independent of 1 time domain boundary integral operators for wave propagation problems have laplace transforms that satisfy bounds of the above type numerical examples from acoustic scattering show that the theory describes accurately the convergence behaviour of runge kutta convolution quadrature for this class of applications our results show in particular that the full classical order of the runge kutta method is attained away from the scattering boundary

stability analysis for stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotic stability analysis problem is considered for a class of stochastic cohen grossberg neural networks with mixed time delays which consist of both the discrete and distributed time delays based on an lyapunov krasovskii functional and the stochastic stability analysis theory a linear matrix inequality lmi approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square it is shown that the addressed stochastic cohen grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two lmis are feasible where the feasibility of lmis can be readily checked by the matlab lmi toolbox it is also pointed out that the main results comprise some existing results as special cases a numerical example is given to demonstrate the usefulness of the proposed global stability criteria

a parameter free dynamic subgrid scale model for large eddy simulation abstract we present a new dynamic smagorinsky subgrid scale model in which the sole model parameter the filter width ratio is computed dynamically the resulting expression for the filter width ratio is parameter free as difficult to compute filter widths required in earlier models are no longer necessary traditionally the filter width ratio is taken as a constant based on assumptions which do not hold in general for all numerical discretizations previous work has shown that simulation results may strongly depend on the filter width ratio parameter thus motivating its accurate determination the new dynamic model is tested on large eddy simulation of decaying isotropic turbulence on hexahedral tetrahedral and wedge topologies using the stabilized finite element method developed by whiting and jansen c h whiting k e jansen a stabilized finite element method for the incompressible navier stokes equations using a hierarchical basis int j numer methods fluids 35 2001 93 116

implicit large eddy simulation of non wall bounded turbulent flows based on the multiscale properties of a high order finite volume method in this paper it is presented the application of a higher order finite volume method based on moving least squares approximations fv mls to the resolution of non wall bounded compressible turbulent flows our approach is based on the monotonically implicit large eddy simulation miles the main idea of miles methodology is the absence of any explicit subgrid scale sgs model in the numerical algorithm to solve turbulent flows in the case of the fv mls method we take advantage of the multiresolution properties of moving least squares approximations and we show that they can be used as an implicit sgs model the numerical results are encouraging the third order fv mls method is able to reproduce the inertial subrange and it obtains better results than other usual numerical schemes in les computations such as the muscl scheme we note that in the present state of this research the numerical method is not yet suited for wall bounded flows this paper is the first step in the application of the fv mls method to general turbulent flows

a new finite element formulation for computational fluid dynamics x the compressible euler and navier stokes equations a space time element method is presented for solving the compressible euler and navier stokes equations the proposed formulation includes the variational equation predictor multi corrector algorithms and boundary conditions the variational equation is based on the time discontinuous galerkin method in which the physical entropy variables are employed a least squares operator and a discontinuity capturing operator are added resulting in a high order accurate and unconditionally stable method implicit explicit predictor multi corrector algorithms applicable to steady as well as unsteady problems are presented techniques are developed to enhance their efficiency implementation of boundary conditions is addressed in particular a technique is introduced to satisfy nonlinear essential boundary conditions and a consistent method is presented to calculate boundary fluxes numerical results are presented to demonstrate the performance of the method

dynamic analysis of stochastic cohen grossberg neural networks with time delays abstract in this paper we discuss stochastic cohen grossberg neural networks with time delays by constructing suitable lyapunov functional and employing the semimartingale convergence theorem we give some sufficient criteria ensuring almost sure exponential stability of the networks the results obtained are helpful to design stability of networks when stochastic noise is taken into consideration

time domain boundary integral equation modeling of heat transmission problems this paper investigates the numerical modeling of a time dependent heat transmission problem by the convolution quadrature boundary element method it introduces the latest theoretical development into the error analysis of the numerical scheme semigroup theory is applied to obtain stability in the spatially semidiscrete scheme functional calculus is employed to yield convergence in the fully discrete scheme we compare the results to a more traditional laplace domain approach

boundedness and stability for cohen grossberg neural network with time varying delays abstract in this paper a model is considered to describe the dynamics of cohen grossberg neural network with variable coefficients and time varying delays uniformly ultimate boundedness and uniform boundedness are studied for the model by utilizing the hardy inequality combining with the halanay inequality and the lyapunov functional method some new sufficient conditions are derived for the model to be globally exponentially stable the activation functions are not assumed to be differentiable or strictly increasing moreover no assumption on the symmetry of the connection matrices is necessary these criteria are important in signal processing and the design of networks

construction of stabilization operators for galerkin least squares discretizations of compressible and incompressible flows the design and analysis of a class of stabilization operators suitable for space time galerkin least squares finite element discretizations of the symmetrized compressible navier stokes equations is discussed the obtained stabilization matrix is well defined in the incompressible limit and reduces to the matrix described in m polner j j w van der vegt and r m j van damme analysis of stabilization operators for galerkin least squares discretizations of the incompressible navier stokes equations comput meth appl mech eng 195 2006 982 1006 the stabilization matrix is investigated to give necessary and sufficient conditions for its positive definiteness under these conditions on the stabilization matrix the galerkin least squares method for the symmetrized compressible navier stokes equations satisfies the entropy condition which ensures global nonlinear stability of the discretization

runge kutta methods for parabolic equations and convolution quadrature we study the approximation properties of runge kutta time discretizations of linear and semilinear parabolic equations including incompressible navier stokes equations we derive asymptotically sharp error bounds and relate the temporal order of convergence which is generally noninteger to spatial regularity and the type of boundary conditions the analysis relies on an interpretation of runge kutta methods as convolution quadratures in a different context these can be used as efficient computational methods for the approximation of convolution integrals and integral equations they use the laplace transform of the confolution kernal via a discrete operational calculus 23 refs 2 tabs

a generalized α method for integrating the filtered navier stokes equations with a stabilized finite element method abstract a generalized method is developed and analyzed for linear first order systems the method is then extended to the filtered navier stokes equations within the context of a stabilized finite element method the formulation is studied through the application to laminar flow past a circular cylinder and turbulent flow past a long transverse groove the method is formulated to obtain a second order accurate family of time integrators whose high frequency amplification factor is the sole free parameter such an approach allows the replication of midpoint rule zero damping gear s method maximal damping or anything in between

convolution quadrature and discretized operational calculus ii operational quadrature rules are applied to problems in numerical integration and the numerical solution of integral equations singular integrals power and logarithmic singularities finite part integrals multiple timescale convolution volterra integral equations wiener hopf integral equations frequency domain conditions which determine the stability of such equations can be carried over to the discretization

a stabilized finite element method for computing turbulence abstract for many flows reynold averaged navier stokes simulation ranss techniques do not give an acceptable description of the flow in these cases a more detailed simulation of the turbulence is required one such detailed simulation technique large eddy simulation les has matured to the point of application to complex flows historically these simulations have been carried out with structured grids which suffer from two major difficulties the extension to higher reynolds numbers leads to an impractical number of grid points and most real world flows are rather difficult to represent geometrically with structured grids unstructured grid methods offer a release from both of these constraints herein we describe the development and validation of a massively parallel stabilized finite element method for les

a spectral collocation method for the navier stokes equations abstract a fourier chebyshev spectral method for the incompressible navier stokes equations is described it is applicable to a variety of problems including some with fluid properties which vary strongly both in the normal direction and in time in this fully spectral algorithm a preconditioned iterative technique is used for solving the implicit equations arising from semi implicit treatment of pressure mean advection and vertical diffusion terms the algorithm is tested by applying it to hydrodynamic stability problems in channel flow and in external boundary layers with both constant and variable viscosity

stabilization and shock capturing parameters in supg formulation of compressible flows abstract the streamline upwind petrov galerkin supg formulation is one of the most widely used stabilized methods in finite element computation of compressible flows it includes a stabilization parameter that is known as typically the supg formulation is used in combination with a shock capturing term that provides additional stability near the shock fronts the definition of the shock capturing term includes a shock capturing parameter in this paper we describe for the finite element formulation of compressible flows based on conservation variables new ways for determining the and the shock capturing parameter the new definitions for the shock capturing parameter are much simpler than the one based on the entropy variables involve less operations in calculating the shock capturing term and yield better shock quality in the test computations

multistep and multistage convolution quadrature for the wave equation algorithms and experiments we describe how a time discretized wave equation in a homogeneous medium can be solved by boundary integral methods the time discretization can be a multistep runge kutta or a more general multistep multistage method the resulting convolutional system of boundary integral equations belongs to the family of convolution quadratures of lubich the aim of this work is twofold it describes an efficient robust and easily parallelizable method for solving the semidiscretized system the resulting algorithm has the main advantages of time stepping methods and of fourier synthesis at each time step a system of linear equations with the same system matrix needs to be solved yet computations can easily be done in parallel the computational cost is almost linear in the number of time steps and only the laplace transform of the time domain fundamental solution is needed the new aspect of the algorithm is that all this is possible without ever explicitly constructing the weights of the convolution quadrature this approach also readily allows the use of modern data sparse techniques to efficiently perform computation in space we investigate theoretically and numerically to which extent hierarchical matrix mathcal h matrix techniques can be used to speed up the space computation the second aim of this article is to perform a series of large scale 3d experiments with a range of multistep and multistage time discretization methods the backward difference formula of order 2 bdf2 the trapezoid rule and the 3 stage radau iia methods are investigated in detail one of the conclusions of the experiments is that the radau iia method often performs overwhelmingly better than the linear multistep methods especially for problems with many reflections yet in connection with hyperbolic problems bdfs have so far been predominant in the literature on convolution quadrature

a fully coupled rans spalart allmaras supg formulation for turbulent compressible flows on stretched unstructured grids abstract when high reynolds turbulent flows are combined with complex and large size geometries computers are no longer enough powerful to deal with direct numerical simulation dns and with the resolution of all the scales of turbulence motion therefore the rans approaches solve averaged equations and use a model to simulate these scales this model contains dissipation processes that should not be polluted by the numerical diffusion needed to stabilized approximations for convection dominated flows in this paper we proposed a strongly coupled numerical formulation for the spalart allmaras model in the framework of stabilized finite element methods computations are performed for compressible newtonian fluids 2d and 3d on unstructured grids of high aspect ratio results are compared with experimental data and also with solutions obtained by different numerical strategies

time accurate consistently stabilized mesh free methods for convection dominated problems this is the pre peer reviewed version of the following article huerta a fernandez s time accurate consistently stabilized mesh free methods for convection dominated problems international journal for numerical methods in engineering gener 2003 vol 56 num 9 p 1225 1242 which has been published in final form at http www3 interscience wiley com journal 102522343 abstract

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

an efficient galerkin boundary element method for the transient heat equation we present boundary integral representations of several initial boundary value problems related to the heat equation a galerkin discretization with piecewise constant functions in time and piecewise linear functions in space leads to optimal a priori error estimates provided that the meshwidths in space and time satisfy h t mathcal o h x 2 each time step involves the solution of a linear system whose spectral condition number is independent of the refinement under the same assumption on the mesh we show that if the parabolic multipole method is used to apply parabolic boundary integral operators the overall complexity of the scheme is log linear while preserving the convergence of the galerkin discretization method the theoretical estimates are confirmed numerically at the end of the paper

a globally convergent matrix free algorithm for implicit time marching schemes arising in finite element analysis in fluids a solution procedure for solving nonlinear time marching problems is presented the nonsymmetric systems of equations arising from a newton type linearization of these time marching problems are solved using an iterative strategy based on the generalized minimal residual gmres algorithm matrix free techniques leading to reduction in storage are presented incorporation of a linesearch algorithm in the newton gmres scheme is discussed an automatic time increment control strategy is developed to increase the stability of the time marching process high speed flow computations demonstrate the effectiveness of these algorithms

a unified approach to compressible and incompressible flows abstract we present a finite element formulation for solving the compressible navier stokes equations which accommodates the use of any set of variables if primitive variables p u t or entropy variables are used the incompressible limit is well behaved therefore one formulation can be used to solve both compressible and incompressible flows

time dependent subgrid scales in residual based large eddy simulation of turbulent channel flow the present study investigates the effect of taking into account the time dependency of the fine subgrid scales in a residual based variational multiscale approach for large eddy simulation the residual based variational multiscale method with time dependent dynamic subgrid scales is presented and the impact of the time dependency is studied for the well known test case of turbulent channel flow results are presented from computations for various values of the reynolds number namely ret 180 ret 395 and ret 590 and several time step sizes a generalized a time integration scheme is employed results from our numerical experiments with dynamic subgrid scales are compared to results obtained with an approximation not explicitly taking the time dependency of the subgrid scales into account for all re t values and time step sizes under consideration results for resolved quantities computed by both approaches are very similar this statement applies to both mean streamwise velocity and root mean square velocity fluctuations however it provides a model for the subgrid scales not depend ing on the time step size and enabling a more robust representation of unresolved scales thus we conclude that the time dependent subgrid scale approximation is not capable of producing more accurate results for this type of flow if the time step size is chosen within an optimal range however we expect it to be more advantageous for more complex problems since our results indicate that it provides a more reliable representation of unresolved scales

convergence of nonautonomous cohen grossberg type neural networks with variable delays this paper is concerned with the global convergence of the solutions of a nonautonomous system with variable delays arising from the description of the states of neurons in delayed cohen grossberg type in a time varying situation by exploring intrinsic features between nonautonomous system and its asymptotic equation several novel sufficient conditions are established to ensure that all solutions of the networks converge to a periodic function or a constant vector for delayed cohen grossberg type neural network nn models in time varying situation the results can be applied directly to group of nns models including hopfield nns bidirectional association memory nns and cellular nns our results are not only presented in terms of system parameters and can be easily verified but also are less restrictive than previously known criteria numerical simulations have also been presented to demonstrate the theoretical analysis

boundary integral solvers for an evolutionary exterior stokes problem this paper proposes and analyzes a full discretization of the exterior transient stokes problem with dirichlet boundary conditions the method is based on a single layer boundary integral representation using galerkin semidiscretization in the space variables and multistep convolution quadrature in time convergence estimates are based on a laplace domain analysis which translates into a detailed study of the exterior brinkman problem some numerical experiments are provided

a variational multiscale method for incompressible turbulent flows bubble functions and fine scale fields this paper presents a residual based turbulence model for the incompressible navier stokes equations the method is derived employing the variational multiscale vms framework a multiscale decomposition of the continuous solution and a priori unique decomposition of the admissible spaces of functions lead to two coupled nonlinear problems termed as the coarse scale and the fine scale sub problems the fine scale velocity field is assumed to be nonlinear and time dependent and is modeled via the bubble functions approach applied directly to the fine scale sub problem a significant contribution in this paper is a systematic and consistent derivation of the fine scale variational operator commonly termed as the stabilization tensor that possesses the right order in the advective and diffusive limits and variationally projects the fine scale solution onto the coarse scale space a direct treatment of the fine scale problem via bubble functions offers several fine scale approximation options with varying degrees of mathematical sophistication that are investigated via benchmark problems numerical accuracy of the proposed method is shown on a forced isotropic turbulence problem statistically stationary turbulent channel flow problems at ret 395 and 590 and non equilibrium turbulent flow around a cylinder at re 3 900