a kernel free particle finite element method for hypervelocity impact simulation an improved hybrid particle finite element method has been developed for the simulation of hypervelocity impact problems unlike alternative methods the revised formulation computes the density without reference to any kernel or interpolation functions for either the density or the rate of dilatation this simplifies the state space model and leads to a significant reduction in computational cost the improved method introduces internal energy variables as generalized co ordinates in a new formulation of the thermomechanical lagrange equations example problems show good agreement with exact solutions in one dimension and good agreement with experimental data in a three dimensional simulation copyright 2005 john wiley sons ltd

on the convergence of a finite element method for a nonlinear hyperbolic conservation law we consider a space time finite element discretization of a time dependent nonlinear hyperbolic conservation law in one space dimension burgers equation the finite element method is higher order accurate and is a petrov galerkin method based on the so called streamline diffusion modification of the test functions giving added stability we first prove that if a sequence of finite element solutions converges boundedly almost everywhere as the mesh size tends to zero to a function u then u is an entropy solution of the conservation law this result may be extended to systems of conservation laws with convex entropy in several dimensions we then prove using a compensated compactness result of murat tartar that if the finite element solutions are uniformly bounded then a subsequence will converge to an entropy solution of burgers equation we also consider a further modification of the test functions giving a method with improved shock capturing finally we present the results of some numerical experiments

a symmetric formulation for computing transient shallow water flows abstract the shallow water equations fall into the category of symmetric advective diffusive systems with source terms these types of equations can be very effectively solved using stabilized methods such as supg and gls a semi discrete finite element method based on these ingredients is presented for the computation of transient shallow water flows special care has been taken in the design of the operators in order to improve the performance for unsteady calculations the solution is advanced in time via a predictor multi corrector algorithm which includes as special cases the second order trapezoidal rule a first order explicit method and a first order implicit method equivalent to the constant in time element of the space time formulation

smoothed particle hydrodynamics stability analysis abstract sph smoothed particle hydrodynamics is a gridless lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze large deformation events recent tests of the standard sph method using the cubic b spline kernel indicated the possibility of an instability in the tensile regime even though no such difficulties were observed in compression a von neumann stability analysis of the sph algorithm has been carried out which identifies the criterion for stability or instability in terms of the stress state and the second derivative of the kernel function the analysis explains the observation that the method is unstable in tension while apparently stable in compression but shows that it is possible to construct kernel functions which are stable in tension and unstable in compression the instability is shown to result from an effective stress with a negative modulus imaginary sound speed being produced by the interaction between the constitutive relation and the kernel function and is not caused by the numerical time integration algorithm that is changes in the effective stress act to amplify rather than reduce perturbations in the strain the analysis and the stability criterion provide insight into possible methods for removing the instability

further results on the stabilizing property of certainty equivalent controllers the conditions which guarantee the stabilization of stochastic parameter systems by infinite horizon certainty equivalent controllers are generalized to the case of random matrices with possibly correlated elements the same conditions are shown to be sufficient for stabilizability by the corresponding optimal controllers

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

multi scale meshfree parallel computations for viscous compressible flows in this paper a petrov galerkin formulation for a viscous compressible fluid using the meshless reproducing kernel particle method rkpm is first presented the location of shocks is determined from the high scale part of the solution using multiresolution analysis a parallel computer implementation for distributed memory architectures is then proposed including a discussion of handling boundary conditions in parallel preliminary results for 1 16 processors of an ibm sp computer are presented and future directions for a massively parallel implementation are outlined

on inf sup stabilized finite element methods for transient problems we consider the behavior of inf sup stabilization in the context of transient problems with multiple time scales our motivation for studying this setting is provided by reacting flows problems for which small time steps are necessary in the integration process we show that for algorithms defined through a process wherein spatial and temporal discretizations are separated the coupling of implicit time integration with spatial inf sup stabilization may lead to anomalous pressure behavior including the onset of spurious oscillations for very small time steps effectively this coupling introduces a stability criterion resulting in a dependence between the spatial grid size and the time step we illustrate our theoretical results by numerical examples that demonstrate the stability criterion 2004 elsevier b v all rights reserved

convergence of a shock capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions convergence of a shock capturing streamline diffusion nite element method for a conservation law in two space dimensions

brief stochastic optimal control and analysis of stability of networked control systems with long delay in this paper stochastic optimal controllers of networked control systems whose network induced delay is longer than a sampling period are designed for the two cases of the system with either full state information or partial state information the controllers are shown to render corresponding networked control systems exponentially mean square stable the optimal estimator of the system state is presented when the system has partial state information and network induced delay is longer than a sampling period the separation theorem is proved to still hold in such networked control systems

stability of the supg finite element method for transient advection diffusion problems implicit time integration coupled with supg discretization in space leads to additional terms that provide consistency and improve the phase accuracy for convection dominated flows recently it has been suggested that for small courant numbers these terms may dominate the streamline diffusion term ostensibly causing destabilization of the supg method while consistent with a straightforward finite element stability analysis this contention is not supported by computational experiments and contradicts earlier von neumann stability analyses of the semidiscrete supg equations this prompts us to re examine finite element stability of the fully discrete supg equations a careful analysis of the additional terms reveals that regardless of the time step size they are always dominated by the consistent mass matrix consequently supg cannot be destabilized for small courant numbers numerical results that illustrate our conclusions are reported

singular foliations with trivial canonical class this paper describes the structure of singular codimension one foliations with numerically trivial canonical bundle on complex projective manifolds

on the symmetric form of systems of conservation laws with entropy abstract this paper reviews the symmetrizability of systems of conservation laws which possess entropy functions symmetric formulations in conservation form for the equations of gas dynamics are presented

a stabilized and coupled meshfree meshbased method for the incompressible navier stokes equations part i stabilization abstract a stabilized meshfree galerkin method is employed for the approximation of the incompressible navier stokes equations in eulerian or arbitrary lagrangian eulerian ale formulation equal order interpolations for velocities and pressure are used it is well known from the meshbased context i e from finite volume and finite element methods that in convection dominated flow problems in eulerian or ale formulation stabilization is a crucial requirement for reliable solutions also stabilization is needed in order to enable equal order interpolations of the incompressible navier stokes equations standard stabilization techniques developed in a meshbased context are extended to meshfree methods it is found that the same structure of the stabilization schemes may be used however the aspect of the stabilization parameter weighting the stabilization terms has to be reconsidered in part ii of this work the resulting stabilized meshfree galerkin method is coupled with a stabilized finite element method the resulting coupled method employs the comparatively costly meshfree galerkin method only where it is needed i e in areas of the domain where a mesh is difficult to maintain and the efficient meshbased finite element method is used in the rest of the domain the fluid solver resulting from this technique is able to solve complex flow problems involving large deformations of the physical domain and or moving and rotating obstacles

improving stability of stabilized and multiscale formulations in flow simulations at small time steps abstract the objective of this paper is to show that use of the element vector based definition of stabilization parameters introduced in t e tezduyar computation of moving boundaries and interfaces and stabilization parameters int j numer methods fluids 43 2003 555 575 t e tezduyar y osawa finite element stabilization parameters computed from element matrices and vectors comput methods appl mech engrg 190 2000 411 430 circumvents the well known instability associated with conventional stabilized formulations at small time steps we describe formulations for linear advection diffusion and incompressible navier stokes equations and test them on three benchmark problems advection of an l shaped discontinuity laminar flow in a square domain at low reynolds number and turbulent channel flow at friction velocity reynolds number of 395

on the effect of temporal error in high order simulations of unsteady flows abstract the present paper focuses on the effect that temporal error has on unsteady solutions modeled with a high spatial order finite element streamline upwind petrov galerkin solver six l stable first through fourth order time integration methods are discussed and exercised on two canonical test cases the convecting isentropic vortex and the two dimensional circular cylinder in crossflow all results are shown on grids composed of p2 third order elements the isentropic vortex case is used to verify temporal order of accuracy assess the relative split between dissipative and dispersive errors for each method with various time steps and quantify the relative computational cost of each method the results from the two dimensional circular cylinder in crossflow simulations at various reynolds numbers are compared to experimental results and accepted numerical results for vortex shedding frequency strouhal number mean drag coefficient and rms lift and drag coefficient the convergence of those parameters with respect to time step size is shown these results highlight the benefits of high order greater than second order time integration methods and the need for time step convergence studies on unsteady simulations

stable boundary conditions and difference schemas for navier stokes equations the navier stokes equations at high reynolds numbers can be viewed as an incompletely elliptic perturbation of the euler equations by using the entropy function for the euler equations as a measure of energy for the navier stokes equations we are able to obtain nonlinear energy estimates for the mixed initial boundary value problem these estimates are used to derive boundary conditions that guarantee l 2 boundedness even when the reynolds number tends to infinity finally we propose a new difference scheme for modeling the navier stokes equations in multidimensions for which we are able to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation

element free galerkin method for wave propagation and dynamic fracture abstract element free galerkin method efg is extended to dynamic problems efg method which is based on moving least square interpolants mls requires only nodal data no element connectivity is needed this makes the method particularly attractive for moving dynamic crack problems since remeshing can be avoided in contrast to the earlier formulation for static problems by authors the weak form of kinematic boundary conditions for dynamic problems is introduced in the implementation to enforce the kinematic boundary conditions with this formulation the stiffness matrix is symmetric and positive semi definite and hence the consistency conergence and stability analyses of time integration remain the same as those in finite element method numerical examples are presented to illustrate the performance of this method the relationship between the element free galerkin method and the smooth particle hydrodynamics sph method is also discussed in this paper results are presented for some one dimensional problems and two dimensional problems with static and moving cracks

stabilized finite element methods for steady advection diffusion with production abstract finite element methods for solving equations of steady advection diffusion with production are constructed employing a linear source to model production the galerkin method requires relatively fine meshes to retain an acceptable degree of accuracy for wide ranges of values of the physical coefficients numerous criteria for improved accuracy via galerkin least squares are proposed and examined in the entire parameter space of these several provide the lowest error in nodal amplification factors each in a certain range of ratios of physical coefficients guidelines for required mesh resolutions are presented for galerkin and galerkin least squares showing that in large parts of the parameter space substantial savings may be obtained by employing galerkin least squares galerkin least squares gradient least squares a new variation of the galerkin method is designed to provide exact nodal amplification factors offering accurate solutions at any resolution numerical tests validate these conclusions

on the stabilization parameter in the subgrid scale approximation of scalar convection diffusion reaction equations on distorted meshes abstract in this paper we revisit the definition of the stabilization parameter in the finite element approximation of the convection diffusion reaction equation the starting point is the decomposition of the unknown into its finite element component and a subgrid scale that needs to be approximated in order to incorporate the distortion of the mesh into this approximation we transform the equation for the subgrid scale within each element to the shape regular reference domain the expression for the subgrid scale arises from an approximate fourier analysis and the identification of the wave number direction where instabilities are most likely to occur the final outcome is an expression for the stabilization parameter that accounts for anisotropy and the dominance of either convection or reaction terms in the equation

a variational multiscale stabilized finite element method for the solution of the euler equations of nonhydrostatic stratified flows we present a compressible version of the variational multiscale stabilization vms method applied to the finite element fe solution of the euler equations for nonhydrostatic stratified flows this paper is meant to verify how the algorithm performs when solving problems in the framework of nonhydrostatic atmospheric dynamics this effort is justified by the previously observed good performance of vms and by the advantages that a compact galerkin formulation offers on massively parallel architectures a paradigm for both computational fluid dynamics cfd and numerical weather prediction nwp practitioners we also propose a simple technique to construct a well balanced approximation of the dominant hydrostatics that if not properly discretized may cause unacceptable vertical oscillations this is a relevant problem in nwp especially in the proximity of steep topography to evaluate the performance of the method for stratified environments six standard 2d and two 3d test cases are selected of these two admit a semi analytic solution while the remaining six are non steady and non linear thermal problems with dominant buoyancy effects that challenge the algorithm in terms of stability

hamiltonian formulation of the variable h sph equations in this paper a variational formulation of smooth particle hydrodynamics for dynamic problems is presented the resulting equations treat the continuum as a hamiltonian system of particles where the constitutive equation of the material is represented via an internal energy term in the case of fluids the internal energy term is a function of density the new formulation introduces a variable smoothing length for the evaluation of density and incorporates a consistent approach for the treatment of rigid boundaries the method overcomes some problems faced by standard sph approaches that use constant smoothing lengths and provides a variational context for a variable smoothing length formulation a numerical example shows the capabilities of this novel formulation

discrete lagrange equations for reacting thermofluid dynamics in arbitrary lagrangian eulerian frames abstract interest in the development of multiscale methods has focused attention on the marked differences in the numerical modeling techniques typically applied at different scales most continuum dynamics models construct approximate solutions to partial differential equations while most nanoscale models employ a discrete hamiltonian approach previous research has demonstrated that the introduction of entropies or internal energies as generalized coordinates along with separation of the discretization and model formulation steps allows general thermomechanical models to be developed at the continuum scale using a nonholonomic hamiltonian or lagrange equation formulation with the introduction of additional state variables and nonholonomic constraints the latter work may be further extended in order to model reacting systems employing a finite element interpolation and a lagrangian an eulerian or an ale mesh the new formulation has been validated by solving several one dimensional reacting shock physics problems the result is a continuum dynamics modeling approach highly compatible with the discrete energy methods normally used at the nanoscale

a particle method for history dependent materials abstract a broad class of engineering problems including penetration impact and large rotations of solid bodies causes severe numerical problems for these problems the constitutive equations are history dependent so material points must be followed this is difficult to implement in a eulerian scheme on the other hand purely lagrangian methods typically result in severe mesh distortion and the consequence is ill conditioning of the element stiffness matrix leading to mesh lockup or entanglement remeshing prevents the lockup and tangling but then interpolation must be performed for history dependent variables a process which can introduce errors proposed here is an extension of the particle in cell method in which particles are interpreted to be material points that are followed through the complete loading process a fixed eulerian grid provides the means for determining a spatial gradient because the grid can also be interpreted as an updated lagrangian frame the usual convection term in the acceleration associated with eulerian formulations does not appear with the use of maps between material points and the grid the advantages of both eulerian and lagrangian schemes are utilized so that mesh tangling is avoided while material variables are tracked through the complete deformation history example solutions in two dimensions are given to illustrate the robustness of the proposed convection algorithm and to show that typical elastic behavior can be reproduced also it is shown that impact with no slip is handled without any special algorithm for bodies governed by elasticity and strain hardening plasticity

robustness of discrete time systems for unstructured stochastic perturbations several stochastic stability robustness measures are presented for nominally exponentially stable linear discrete time systems with unstructured perturbations having second moment bounds dependence of these measures on the stability degree of the nominal system and other parameters used in the procedure is illustrated by using the time evolution of the second moment of the system state and stochastic lyapunov stability results positive super martingale convergence theorems the ability of nominally exponentially stable systems to maintain stability in the presence of unstructured stochastic linear and nonlinear perturbations is demonstrated quantitative results are given to determine the maximum modeling uncertainty which can be tolerated in design upper bounds on the second moments of stochastic perturbations to maintain the mean square and almost sure stability of these systems in the presence of unstructured perturbations are obtained

energy preservation and entropy in lagrangian space and time staggered hydrodynamic schemes usual space and time staggered sts leap frog lagrangian hydrodynamic schemes such as von neumann richtmyer s 1950 wilkins 1964 and their variants are widely used for their simplicity and robustness despite their known lack of exact energy conservation since the seminal work of trulio and trigger 1950 and despite the later corrections of burton 1991 it is generally accepted that these schemes cannot be modified to exactly conserve energy while retaining all of the following properties sts stencil with velocities half time centered with respect to positions explicit second order algorithm locally implicit for internal energy and definite positive kinetic energy it is shown here that it is actually possible to modify the usual sts hydrodynamic schemes in order to be exactly energy preserving regardless of the evenness of their time centering assumptions and retaining their simple algorithmic structure burton s conservative scheme 1991 is found as a special case of time centering which cancels the term here designated as incompatible displacements residue in contrast von neumann richtmyer s original centering can be preserved provided this residue is properly corrected these two schemes are the only special cases able to capture isentropic flow with a third order entropy error instead of second order in general the momentum equation is presently obtained by application of a variational principle to an action integral discretized in both space and time the internal energy equation follows from the discrete conservation of total energy entropy production by artificial dissipation is obtained to second order by a prediction correction step on the momentum equation the overall structure of the equations explicit for momentum locally implicit for internal energy remains identical to that of usual sts leap frog schemes though complementary terms are required to correct the effects of time step changes and artificial viscosity updates in deriving these schemes an apparently novel approach of flux in time was introduced to correct numerical residues and ensure energy conservation this method can be applied to essentially any numerical scheme whenever required or desired provided space and time numerical consistency is preserved numerical test cases are presented confirming the conservative character of the new csts schemes down to computer round off errors and showing various improvements compared to the standard von neumann richtmyer and wilkins sts schemes mostly on shock levels shock velocities singularity induced distortions and cfl stability limits

a positivity preserving variational method for multi dimensional convectiondiffusionreaction equation a new positivity preserving variational ppv procedure is proposed to solve the convectiondiffusionreaction cdr equation through the generalization of stabilized finite element methods the present variational procedure offers minimal phase and amplitude errors for different regimes associated with convection diffusion and reaction effects by means of fourier analysis we first review the shortcomings of the galerkin least squares gls and the subgrid scale sgs methods during the change in sign of the reaction coefficient that motivates us for the present linear stabilization as a combined gls sgs methodology discrete upwind operator with a solution dependent nonlinear term is then introduced in high gradient regions which enables the positivity preserving property in the variational formulation direct extension to multi dimensions is carried out by considering the principle streamline and crosswind directions the efficacy of the method is demonstrated by the systematic accuracy and stability analyses in one and two dimensions results show the reduction of oscillations in the solution in one and two dimensional cases and a remarkable reduction in the phase error is observed for the cases with negative reaction coefficient the proposed formulation provides a superior solution in the reaction dominated as well as the convection dominated regimes due to the minimization of spurious oscillations and accurate capturing of the high gradient regions

liquid vapor phase transition thermomechanical theory entropy stable numerical formulation and boiling simulations abstract we develop a new continuum mechanics modeling framework for liquid vapor flows with particular focus on the van der waals fluid by invoking microforce theory the coleman noll procedure is generalized to derive consistent constitutive relations in the presence of non local effects a new thermodynamically consistent algorithm for the van der waals model is designed using functional entropy variables and a new temporal scheme employing a family of new quadrature rules we show that the resulting fully discrete scheme is unconditionally stable in entropy and second order time accurate isogeometric analysis is utilized for spatial discretization the analytical properties of the formulation are corroborated by benchmark problems three sets of application problems are simulated to demonstrate the capability of the model and the algorithm our methodology provides a particularly useful predictive tool for boiling flows

algebraic integrability of foliations with numerically trivial canonical bundle given a reflexive sheaf on a mildly singular projective variety we prove a flatness criterion under certain stability conditions this implies the algebraicity of leaves for sufficiently stable foliations with numerically trivial canonical bundle such that the second chern class does not vanish combined with the recent works of druel and greb guenancia kebekus this establishes the beauville bogomolov decomposition for minimal models with trivial canonical class

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

implicit finite incompressible elastodynamics with linear finite elements a stabilized method in rate form abstract we propose a stabilization method for linear tetrahedral finite elements suitable for the implicit time integration of the equations of nearly and fully incompressible nonlinear elastodynamics in particular we derive and discuss a generalized framework for stabilization and implicit time integration that can comprehensively be applied to the class of all isotropic hyperelastic models in this sense the presented development can be considered an important extension and complement to the stabilization approach proposed by the authors in previous work which was instead focused on explicit time integration and simple neo hookean models for nearly incompressible elasticity with the goal of computational efficiency we also present a two step block gauss seidel strategy for the time update of displacements velocities and pressures specifically a mixed system of equations for the velocity and pressure is updated implicitly in a first stage and the displacements are updated explicitly in a second stage the proposed mixed formulation is then embedded in newton type strategies for the nonlinear solution of the equations of motion various implicit time integration strategies are considered and particularly we focus on high frequency dissipation time integrators which are preferable in transient mechanics applications an extensive set of numerical computations with linear tetrahedral elements is presented to demonstrate the performance of the proposed approach

h adaptive stabilized finite element solver for calculation of generalized aerodynamic forces a finite element method based on the streamline upwind petrov galerkin stabilization technique is developed to solve the compressible euler equations the method is extended for computing unsteady small disturbances in the flow domain as a result of boundary motion which is applied through the linearized solid wall boundary condition the method is able to calculate the frequency dependent generalized aerodynamic forces without any need for deformation of mesh inside the flow domain error estimates are used to drive automated h refinement of mesh for steady state and frequency domain calculations steady state solutions and generalized aerodynamic forces are compared to benchmark data for transonic and supersonic mach numbers the results show that the presence of shocks in the flow makes it difficult to use a single mesh for all computations including the linearized flow the h refinement procedure is shown to be an effective way of ensuring reliable computations for the nonlinear and linearized solve

discrete hamilton s equations for viscous compressible fluid dynamics abstract lagrange s and hamilton s equations are used extensively in numerical modeling of rigid body dynamics and continuum solid dynamics problems the use of energy methods in viscous compressible flow problems has been by contrast rather limited largely confined to the development of basic balance laws in partial differential equation form however finite element interpolation of the modeled flow field allows for the direct application of the discrete form of hamilton s equations to viscous compressible fluid dynamics in eulerian frames the resulting model is a true energy formulation developed without reference to the partial differential balance equations which underlie conventional finite difference weighted residual finite element and finite volume methods

infinite horizon optimal control of linear discrete time systems with stochastic parameters the infinite horizon optimal control problem is considered in the general case of linear discrete time systems and quadratic criteria both with stochastic parameters which are independent with respect to time a stronger stabilizability property and a weaker observability property than usual for deterministic systems are introduced it is shown that the infinite horizon problem has a solution if the system has the first property if in addition the problem has the second property the solution is unique and the control system is stable in the mean square sense a simple necessary and sufficient condition explicit in the system matrices is given for the system to have the stronger stabilizability property this condition also holds for deterministic systems to be stabilizable in the usual sense the stronger stabilizability and weaker observability properties coincide with the usual ones if the parameters are deterministic

stabilization of deterministic and stochastic parameter discrete systems a class of suboptimal control laws having the stabilizing property is used for treating linear discrete time systems with deterministic and stochastic parameters known stabilization results in the deterministic case are extended to systems with singular state transition matrices and optimization horizon lengths shorter than the controllability indices of these systems it is shown that in the case where the state transition and input matrices contain stochastic components the stabilization of these systems in the sense of both almost sure asymptotic and mean square exponential stability is possible using the same line of reasoning

a space time finite element method for structural acoustics in infinite domains part 1 formulation stability and convergence abstract a space time finite element method for solution of the exterior structural acoustics problem involving the interaction of vibrating elastic structures submerged in an infinite acoustic fluid is formulated in particular time discontinuous galerkin and galerkin least squares gls variational formulations for coupled structural acoustics in unbounded domains are developed and analyzed for stability and convergence the formulation employs a finite computational fluid domain surrounding the structure and incorporates time dependent non reflecting boundary conditions on the fluid truncation boundary energy estimates are obtained which allow us to prove the unconditional stability of the method for the coupled fluid structure problem with absorbing boundaries the methods developed are especially useful for the application of adaptive solution strategies for transient acoustics in which unstructured space time meshes are used to track waves propagating along space time characteristics an important feature of the space time formulation is the incorporation of temporal jump operators which allow for finite element interpolations that are discontinaous in time for additional stability least squares operators based on local residuals of the structural acoustics equations including the non reflecting boundary conditions are incorporated the energy decay estimates and high order accuracy predicted by our a priori error estimates are demonstrated numerically in a simple canonical example

multiscale stabilized solutions to one dimensional systems of conservation laws abstract we present a variational multiscale formulation for the numerical solution of one dimensional systems of conservation laws the key idea of the proposed formulation originally presented by hughes comput methods appl mech engrg 127 1995 387 401 is a multiple scale decomposition into resolved grid scales and unresolved subgrid scales incorporating the effect of the subgrid scales onto the coarse scale problem results in a finite element method with enhanced stability properties capable of accurately representing the sharp features of the solution in the formulation developed herein the multiscale split is invoked prior to any linearization of the equations special attention is given to the choice of the matrix of stabilizing coefficients and the discontinuity capturing diffusion the methodology is applied to the one dimensional simulation of three phase flow in porous media and the shallow water equations these numerical simulations clearly show the potential and applicability of the formulation for solving highly nonlinear nearly hyperbolic systems on very coarse grids application of the numerical formulation to multidimensional problems is presented in a forthcoming paper

hamiltonian particle hydrodynamics abstract particle based hydrodynamics models offer distinct advantages over eulerian and lagrangian hydrocodes in particular shock physics applications particle models are designed to avoid the mesh distortion and state variable diffusion problems which can hinder the effective use of lagrangian and eulerian codes respectively however existing particle in cell and smooth particle hydrodynamics methods employ particles which are actually moving interpolation points the latter distinction has been emphasized in the more recent development of element free galerkin theory as a result general formulations of all of the aforementioned methods are based on the partial differential equation forms of the continuum balance laws which underlie conventional eulerian and lagrangian schemes an alternative modeling methodology based on the application of hamilton s equations to a system of deforming physical particles provides a fully lagrangian energy based approach to shock physics simulations neither interpolations of field variables nor continuum balance laws are used to establish the state equations for the particle system mechanical and thermal interaction of the particles is accounted for by nonholonomic constraints which determine both particle entropy evolution and particle collision loads application of the method is illustrated by simulation of a wall shock problem

control of randomly varying systems with prescribed degree of stability the control of linear discrete time systems with stochastic parameter matrices is discussed two control techniques are particularly used infinite horizon and finite moving horizon optimal regulators it is shown that it is possible to design controllers with a guaranteed degree of exponential stochastic stability by properly modifying the performance indexes in this way the deterministic regulator problem with a prescribed degree of stability is extended to the case of stochastic parameter systems

a stabilized finite element method using a discontinuous level set approach for the computation of bubble dynamics a novel numerical method for solving three dimensional two phase flow problems is presented this method combines a quadrature free discontinuous galerkin method for the level set equation with a pressure stabilized finite element method for the navier stokes equations the main challenge in the computation of such flows is the accurate evaluation of surface tension forces this involves the computation of the curvature of the fluid interface in the context of the discontinuous galerkin method we show that the use of a curvature computed by means of a direct derivation of the level set function leads to inaccurate and oscillatory results a more robust second order least squares computation of the curvature that filters out the high frequencies and produces converged results is presented this whole numerical technology allows to simulate a wide range of flow regimes with large density ratios to accurately capture the shape of the deforming interface of the bubble and to maintain good mass conservation

a multi element group preconditioned gmres algorithm for nonsymmetric systems arising in finite element analysis abstract a multi element group domain decomposition algorithm is presented for solving linear nonsymmetric systems arising in finite element analysis the iterative strategy employed is based on the generalized minimum residual gmres procedure originally proposed by saad and shultz two levels of preconditioning are investigated coding is presented which fully exploits vector architectured computers applications to problems of high speed compressible flow illustrate the effectiveness of the scheme

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

the equivalent discrete time optimal control problem for continuous time systems with stochastic parameters this paper considers the transformation of the digital optimal control problem to an equivalent discrete time optimal control problem for linear continuous time systems with continuous time white stochastic parameters and additive continuous time white noise the observations available at the sampling instants are in general non linear and corrupted by discrete time noise the equivalent discrete time system has white stochastic parameters expressions are derived for the first and second moments of these parameters and for the cost criterion parameters which are explicit in the parameters and the statistics of the continuous time system

provably unconditionally stable second order time accurate mixed variational methods for phase field models we introduce provably unconditionally stable mixed variational methods for phase field models our formulation is based on a mixed finite element method for space discretization and a new second order accurate time integration algorithm the fully discrete formulation inherits the main characteristics of conserved phase dynamics namely mass conservation and nonlinear stability with respect to the free energy we illustrate the theory with the cahn hilliard equation but our method may be applied to other phase field models we also propose an adaptive time stepping version of the new time integration method we present some numerical examples that show the accuracy stability and robustness of the new method

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

a stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows a numerical method for the simulation of three dimensional incompressible two phase flows is presented the proposed algorithm combines an implicit pressure stabilized finite element method for the solution of incompressible two phase flow problems with a level set method implemented with a quadrature free discontinuous galerkin dg method e marchandise j f remacle n chevaugeon a quadrature free discontinuous galerkin method for the level set equation journal of computational physics 212 2006 338 357 the use of a fast contouring algorithm n chevaugeon e marchandise c geuzaine j f remacle efficient visualization of high order finite elements international journal for numerical methods in engineering permits us to localize the interface accurately by doing so we can compute the discontinuous integrals without neither introducing an interface thickness nor reinitializing the level set the capability of the resulting algorithm is demonstrated with large scale numerical examples free surface flows dam break sloshing and small scale ones two phase poiseuille rayleigh taylor instability

a spacetime discontinuous galerkin method for scalar conservation laws abstract we present a spacetime discontinuous galerkin sdg finite element method for scalar hyperbolic conservation laws the method is consistent with the integral forms of the conservation law and its associated entropy condition written in terms of the physical godunov flux on each spacetime element the discrete basis functions are piecewise continuous in spacetime admitting discontinuities across element boundaries the resulting bubnov galerkin method is high order stable for both convex and non convex flux functions it does not require stabilization beyond the basic galerkin projection the sdg method is applicable to both layered and unstructured spacetime grids an element by element solution scheme delivers o n computational complexity where n is the number of elements when applied to spacetime meshes that conform to a special causality constraint we employ two different limiters to control the local overshoot and undershoot that the basic sdg projection generates near shocks

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

the influence of finite word length on digital optimal control this paper is concerned with the performance of linear discrete time systems controlled by a finite word length computer with floating point arithmetic and of which the state is directly measurable with an a d converter of the same word length the effect of using finite word length is twofold first roundings are made after addition or multiplication of two rounded numbers second the control parameters are represented in the controller s memory by rounded numbers the first effect can be accounted for by considering the control parameters stochastic the second effect is deterministic after a description of the stochastlcs of the roundoff errors has been derived the influence of both effects on the optimality and stability of digital control systems in the steady state in relation to a quadratic cost function is considered

on the convergence of shock capturing streamline diffusion finite element methods for hyperbolic conservation laws we extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shock capturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the meh size with this term present we prove a maximum norm bound for finite element solutionsof burgers equation an thus complete an earlier convergence proof for this equation we further prove using entropy variables that a strong limit of finite element solutions is a weak solution of the system of conservation laws and satisfies the entropy inequality asociated with the entropy variables results of some numerical experiments for the time dependent compressible euler equations in two dimensions are also reported

skew selfadjoint form for systems of conservation laws abstract hyperbolic systems of conservation laws augumented with an entropy inequality are studied it is shown that such systems can be written in a quasilinear skew selfadjoint form centered differencing of such a form under the smooth regime ends up with a systematic recipe for constructing quasiconservative schemes where the global entropy conservation is recovered employing the above formulation in bounded regions under the nonsmooth regime as well a local entropy decay estimate is also concluded examples of the shallow water and the full gasdynamics equations are explicitly treated

comparison of some finite element methods for solving the diffusion convection reaction equation abstract in this paper we describe several finite element methods for solving the diffusion convection reaction equation none of them is new although the presentation is non standard in an effort to emphasize the similarities and differences between them in particular it is shown that the classical supg method is very similar to an explicit version of the characteristic galerkin method whereas the taylor galerkin method has a stabilization effect similar to a sub grid scale model which is in turn related to the introduction of bubble functions

non weak strong solutions in gas dynamics a c11 p version stlsfef in lagrangian frame of reference using ρ u p primitive variables in this paper we present computations of the non weak solutions of class c11 of transient navier stokes equations for compressible flow in lagrangian frame of reference using space time least squares finite element formulation with primitive variables u p for high speed compressible flows the solutions reported here possess the same orders of continuity as the governing differential equations the role of diffusion i e viscosity physical or artificial and thermal conductivity on shock structure is demonstrated compression of air in a rigid cylinder by a rigid massless and frictionless piston is used as a model problem true time evolutions of class c11 are reported beginning with the first time step until steady shock conditions are achieved comparisons with analytical solutions are presented when possible copyright 2001 john wiley sons ltd

notes on the stability of non rectangular space time finite elements the method of space time finite elements enables the simple solution of quite new problems it is possible to assume the arbitrary partition of the structure area in each moment of integration of the motion equation instability is caused by a too large time step and too great changes of joint locations in successive time steps a changeable spatial partition is useful in contact dynamic problems in the case of a travelling support generally in problems with movable edges in this paper a stability problem is described and some investigations for chosen types of non rectangular space time finite elements are carried out linear and surface elements which in time space gain an additional time dimension are presented some numerical examples prove the efficiency of the described method under determined limitations

local preconditioning and variational multiscale stabilization for euler compressible steady flow abstract this paper introduces a preconditioned variational multiscale stabilization p vms method for compressible flows in this introductory paper we focus on inviscid flow and steady state problems the euler equations are solved on fully unstructured grids and discretized using the finite element method the p vms method can be decomposed into three parts first a local preconditioner is applied to the continuous equations to reduce the stiffness while covering a wide range of mach numbers then the resulting preconditioned system is discretized in space using finite elements and stabilized with a variational multiscale stabilization method adapted for the preconditioned equations in this paper the solution is advanced in time using a fully explicit time discretization although p vms is general and can be applied to fully implicit solvers the proposed method is assessed by comparing convergence and accuracy of the solutions between the non preconditioned and preconditioned cases in particular for van leer lee roe s 1991 and choi merkle s 1993 preconditioners in some selected examples covering a large range of mach numbers

infinite horizon quadratic optimal control of a class of nonlinear stochastic systems the author considers a class of discrete time nonlinear stochastic control systems whose nonlinearities are described by statistical means by introducing the proper mean square stabilizability and detectability properties of such systems and giving a characterization of these properties in terms of system parameters he examines the steady state properties of quadratically optimal controllers a robustness property of these controllers is pointed out

potential density of rational points on the variety of lines of a cubic fourfold we prove the potential density of rational points on the variety of lines of a sufficiently general cubic fourfold defined over a number field where sufficiently general means that a condition of terasoma type is satisfied these varieties have trivial canonical bundle and have geometric picard number equal to one

on the spannedness of adjunction of vector bundles let x be a smooth projective variety of dimension n defined over the field of complex numbers and e be an ample vector bundle on x the linear system kx c e is called the adjoint bundle for vector bundle e the nefness and the ampleness of the adjoint bundle kx cl e have been investigated by several authors abw f p1 yz in this paper we shall investigate the base point freeness spannedness of the adjoint bundle kx c e i e we ask the following

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

an adaptive variational procedure for the conservative and positivity preserving allen cahn phase field model abstract in this paper we present an adaptive variational procedure for unstructured meshes to capture fluid fluid interfaces in two phase flows the two phases are modeled by the phase field finite element formulation which involves the conservative allen cahn equation coupled with the incompressible navier stokes equations the positivity preserving variational formulation is designed to maintain the bounded and stable solution of the allen cahn equation for the adaptivity procedure we consider the residual based error estimates for the underlying differential equations of the two phase system in particular the adaptive refinement coarsening is carried out by the newest vertex bisection algorithm by evaluating the residual error indicators based on the error estimates of the allen cahn equation the coarsening algorithm avoids the storage of the tree data structures for the hierarchical mesh thus providing the ease of numerical implementation furthermore the proposed nonlinear adaptive partitioned procedure aims at reducing the amount of coarsening while maintaining the convergence properties of the underlying nonlinear coupled differential equations we investigate the adaptive phase field finite element scheme through the spinodal decomposition in a complex curved geometry and the volume conserved interface motion driven by the mean curvature flow for two circles in a square domain we then assess the accuracy and efficiency of the proposed procedure by modeling the free surface motion in a sloshing tank in contrast to the non adaptive eulerian grid counterpart we demonstrate that the mesh adaptivity remarkably reduces the degrees of freedom and the computational cost by nearly half for similar accuracy the mass loss in the allen cahn equation via adaptivity process is also reduced by nearly three times compared to the non adaptive mesh finally we apply the adaptive numerical framework to solve the application of a dam breaking problem with topological changes

a space time galerkin least squares finite element formulation of the navier stokes equations for moving domain problems a space time galerkin least squares finite element formulation of the navier stokes equations is presented for the analysis of free surface flows moving spatial configurations and deforming fluid structure interfaces the variational equation is based on the time discontinuous galerkin method employing the physical entropy variables the space time elements are oriented in time to accommodate the spatial deformations if the elements are oriented along the particle paths the formulation is lagrangian and if they are fixed in time it is eulerian consequently this formulation is analogous to the arbitrary lagrangian eulerian ale technique a novel mesh rezoning strategy is presented to orient the elements in time and adapt the fluid mesh to the changing spatial configuration numerical results are presented to show the performance of the method

analysis of stabilization operators for galerkin least squares discretizations of the incompressible navier stokes equations in this paper we discuss the design and analysis of a class of stabilization operators for space time galerkin least squares finite element discretizations suitable for the incompressible limit of the symmetrized navier stokes equations given in g hauke t j r hughes a comparative study of different sets of variables for solving compressible and incompressible flows comput methods appl mech engrg 153 1998 1 44 this set of equations consists of the incompressible navier stokes equations in combination with the heat equation the analysis results in stabilization operators which are positive definite and dimensionally consistent in addition a detailed proof is given that the space time galerkin least squares discretization together with the proposed stabilization operators satisfies a coercivity condition for the linearized form of the equations this ensures that necessary conditions for uniqueness and stability of the numerical solution are satisfied by the finite element discretization

third order upwind finite element computation of the incompressible navier stokes equations part i computation of flow around rectangular cylinders abstract aerodynamic behaviours of two dimensional unsteady flows around rectangular cylinders are numerically investigated by third order upwind finite element computation of the incompressible navier stokes equations a turbulence model such as the two equation model is not incorporated in the computational scheme so that the rectangular cylinders at depth breadth ratios from 0 7 to 4 to be considered are located in a uniform flow it is found that the numerical results of flows around the rectangular cylinders obtained by using the third order upwind finite element scheme are in good agreement with other computational and experimental results

a discontinuous galerkin method for viscous compressible multifluids abstract we present a generalized discontinuous galerkin method for a multicomponent compressible barotropic navier stokes system of equations the system presented has a functional viscosity which depends on the pressure p p i of the flow with the density and the local concentration i high order runge kutta time discretization techniques are employed and different methods of dealing with arbitrary coupled boundary conditions are discussed analysis of the energy consistency of the scheme is performed in addition to inspection of the relative error of the solution compared to exact analytic test cases finally several examples comparisons generalizations and physical applications are presented

implementation of boundary conditions for meshless methods abstract boundaries and boundary conditions are an aspect of the numerical solution of partial differential equations where meshless methods have had to surmount many initial difficulties due to the lack of a finite element like kronecker delta condition furthermore it is frequently desirable especially in fluid mechanics to impose general nonlinear boundary and interface constraints this paper describes a computationally efficient algorithm based on d alembert s principle that can be used for general constraints both in meshless methods and finite elements first a method of partitioning meshless shape functions suitable for imposing linear boundary conditions is developed subsequently an analogous method is developed for nonlinear constraints special attention is given to imposing general boundary and fluid structure interface conditions on the navier stokes equations in terms of conservative variables numerical results using d alembert s principle with the reproducing kernel particle method rkpm including viscous supersonic flow past a naca 7012 airfoil are shown

discrete hamilton s equations for arbitrary lagrangian eulerian dynamics of viscous compressible flow abstract a number of different arbitrary lagrangian eulerian ale formulations of continuum fluid and solid dynamics problems have been developed to address applications where more conventional lagrangian or eulerian modeling techniques are difficult to apply in general these ale formulations are based on finite difference or weighted residual finite element solutions of the partial differential equations for the system an alternative energy based ale model for fluid dynamics simulations may be obtained by direct application of hamilton s canonical equations to a finite element discretization of an open deforming control volume formulated in terms of convected coordinates and incorporating an adaptive mesh scheme this modeling approach yields a simple but general description of viscous compressible flows numerical application of the method demonstrates accurate results in the solution of several shock problems whether the calculations are performed using a lagrangian an eulerian or an ale mesh

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