on the structural stability of the euler voigt and navier stokes voigt models abstract we consider the euler voigt equations and the navier stokes voigt equations which are obtained by an inviscid regularization from the corresponding equations the main result we show is the structural stability of the system in terms of the variations of both viscosity and regularization parameters

characteristic based time dependent maxwell equation solvers on a general curvilinear frame four cell centered finite volume characteristic based procedures for solving time dependent three dimensional maxwell equations on a general curvilinear frame are developed and implemented on a spherical coordinate system these methods generate simulations or an oscillating electric dipole without wave reflection from the truncated computational domain through a comparative study it is established that an upwind biased third order scheme demonstrates less dispersive and dissipative errors than second order schemes

hydrodynamic modeling of short channel devices using an upwind flux vector splitting scheme upwind flux vector splitting is presented for hydrodynamic modeling of 1d and 2d deep submicron semiconductor devices this approach splits the jacobian matrices of the hydrodynamic system into two parts corresponding to forward and backward running fluxes and an upwind difference is applied to each split flux influences of the boundary discontinuity of electric field and velocity on transport results in the 2d deep submicron devices are discussed the study demonstrates that the developed method is capable of handling large discontinuity of the boundary conditions and highly non linear source terms in short channel semiconductor devices

a genuinely multidimensional convective pressure flux split riemann solver for euler equations a simple inexpensive genuinely multidimensional hll type riemann solver for euler equations of gasdynamics is proposed the genuinely multidimensional formulation is based on the work of balsara 17 in the present approach the missing contact wave in the hll type solver is restored using the hll cps formulation of mandal and panwar 5 a few two dimensional standard test cases are solved to demonstrate the efficacy of the proposed solver a very simple new genuinely multidimensional hll type riemann solver for euler equations is proposed due to the use of closed form expressions for the fluxes the present method is easier to apply the contact discontinuity is restored using the hll cps formulation without the need for independently specifying its direction of evolution numerical test results demonstrate the efficacy of the present method of its ability to capture accurate solutions

weak and strong solutions for the incompressible navier stokes equations with damping in this paper we show that the cauchy problem of the navier stokes equations with damping u 1u 0 has global weak solutions for any 1 global strong solution for any 7 2 and that the strong solution is unique for any 7 2 5

an implicit finite volume method for the solution of 3d low mach number viscous flows using a local preconditioning technique this paper presents a cell centered high order finite volume scheme for the solution of the three dimensional 3d navier stokes equations with low mach number the system of non linear equations is solved by means of a fully implicit pseudo transient scheme each pseudo time step is solved by a newton gmres procedure a local preconditioning technique is used to scale the speed of sound and to improve the system condition number for low mach number and low cell reynolds number this preconditioning is applied to the ausm up flux vector splitting function the method is tested on 2d and 3d low mach number laminar flows

toward a universal adaptive finite element strategy part 3 design of meshes abstract in this third paper in our series the issue of designing h p meshes which are optimal in some sense is addressed criteria for h p meshes are derived which are based on the idea of minimizing the estimated error over a mesh with a fixed number of degrees of freedom an optimization algorithm is developed based on these criteria and is applied to several model one dimensional and two dimensional elliptic boundary value problems numerical results indicate that the approach can lead to exponential rates of convergence

a strong conservative riemann solver for the solution of the coupled maxwell and navier stokes equations the coupled system of the navier stokes and maxwell equations are recast into a strong conservative form which allows the fluid coupling to the maxwell system to be written in terms of flux divergence rather than explicit source terms this effectively removes source terms from the navier stokes equations although retaining an exact coupling to the electromagnetics while this relieves the stiff source terms and potentially stabilizes the system it introduces a much more complicated eigenstructure to the governing equations the flux jacobian and eigenvectors for this strong conservative system are presented in the current paper for the first time an approximate riemann solver based upon these eigenvectors is then introduced and tested the solver is implemented in a preconditioned dual time implicit form validations for classic one and two dimensional problems are presented and the performances of the new formulation and the traditional source coupled formulation are compared

solution adaptive cartesian cell approach for viscous and inviscid flows a cartesian cell based approach for adaptively refined solutions of the euler and navier stokes equations in two dimensions is presented grids about geometrically complicated bodies are generated automatically by the recursive subdivision of a single cartesian cell encompassing the entire flow domain where the resulting cells intersect bodies polygonal cut cells are created using modified polygon clipping algorithms the grid is stored in a binary tree data structure that provides a natural means of obtaining cell to cell connectivity and of carrying out solution adaptive mesh refinement the euler and navier stokes equations are solved on the resulting grids using a finite volume formulation the convective terms are up winded a linear reconstruction of the primitive variables is performed providing input states to an approximate riemann solver for computing the fluxes between neighboring cells the results of a study comparing the accuracy and positivity of two classes of cell centered viscous gradient reconstruction procedures is briefly summarized adaptively refined solutions of the navier stokes equations are shown using the more robust of these gradient reconstruction procedures where the results computed by the cartesian approach are compared to theory experiment and other accepted computational results for a series of low and moderate reynolds number flows

the optimal symmetrical points for polynomial interpolation of real functions in the tetrahedron abstract the main result of this paper is the computation of the mean optimal symmetrical interpolation points in the tetrahedron up to degree 9 this interpoation set has the smallest lebesgue constant known today

a flux splitting method for the euler equations the solution of the euler and navier stokes equations was the focus of this research as with methods such as the ausm family this work further attempted to construct an explicit upwind method that combines both simplicity and accuracy in particular with an appropriate choice of working variables the aim was to develop a simple method that is based on the advection of the characteristic variables the end result is a computationally efficient method valid for all homogeneous fluids with accuracy comparable to that of expensive flux difference splitting methods good performance was extensively verified with riemann test problems and results were on par with roe s scheme furthermore at least one formulation of the method passed all test problems satisfactory without requiring manual intervention the method also illuminates some similarities between flux difference splitting and the ausm family of methods

absorbing boundary conditions for difference approximations to the multi dimensional wave equation construction des conditions aux limites absorbantes pour l equation des ondes multidimensionnelle a l aide d approximations aux differences formulation sous forme canonique des conditions aux limites absorbantes analytiques

a numerical integration scheme for finite element method based on symbolic manipulation this paper is concerned with the improvement of the efficiency and accuracy of the usual numerical integration procedures for the finite element method a modified numerical integration scheme based on both the symbolic manipulation system and the numerical integration formula is proposed its efficiency for the integration of complicated rational or irrational expressions is demonstrated through several numerical examples to verify its effectiveness in the calculation of the finite element stiffness matrix a simple numerical example is also presented

an evaluation of roe s scheme generalizations for equilibrium real gas flows the extension of roe s approximate riemann solver to equilibrium real gas is analyzed by means of a general formulation allowing us to clarify the inherent nonuniqueness of the average state and the influence of the functional form of the equation of state several generalizations of roe s scheme are then reviewed and their numerical performances are discussed by computing some 2d steady hypersonic flows the flow solvers are coupled with a newly developed efficient and robust procedure for thermochemical air properties evaluation all of the tested equilibrium solvers achieve very similar results they are found of comparable numerical efficiency the higher performances being associated with vinokur s and liou s solvers it is concluded that equilibrium simulations in 2d are by no means less robust than the perfect gas ones when coupled with the proposed procedure for properties evaluation

new basis functions and computational procedures for p version finite element analysis new basis functions and solution procedures for p version finite element analysis are described they are used in a highly efficient p version finite element solver for linear elastostatics and dynamics which has been used in an industrial environment for over two years using two sample applications it is shown that using the techniques proposed here p version finite element analysis can have a substantially lower computational cost for given accuracy than standard finite element methods this makes the industrial applicability of p version finite element analysis much wider than is commonly believed

pullback attractors for asymptotically compact non autonomous dynamical systems abstract first we introduce the concept of pullback asymptotically compact non autonomous dynamical system as an extension of the similar concept in the autonomous framework our definition is different from that of asymptotic compactness already used in the theory of random and non autonomous dynamical systems as developed by crauel flandoli kloeden schmalfuss amongst others which means the existence of a random or time dependent family of compact attracting sets next we prove a result ensuring the existence of a pullback attractor for a non autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets this attractor is minimal and in most practical applications it is unique finally we illustrate the theory with a 2d navier stokes model in an unbounded domain

blended ausm method for all speeds and all grid aspect ratios an ausm based discretization method using an explicit third order discretization for the convective part and a line implicit central discretization for the acoustic part and for the diffusive part has been developed for incompressible and low speed compressible navier stokes equations the lines are chosen in the direction of the gridpoints with shortest connection the semi implicit line method is used in multistage form because of the explicit third order discretization of the convective part multigrid is used as acceleration technique because of the implicit treatment of the acoustic and the diffusive terms the stiffness otherwise caused by high aspect ratio cells is removed low mach number stiffness is treated by a preconditioning technique to ensure physical correct behavior of the discretization for vanishing mach number extreme care has been taken for vanishing mach number stabilization terms are added to the mass flux pressure and temperature stabilization terms are necessary the coefficients of these terms are chosen so that correct scaling with mach number is obtained a blend of the low speed algorithm with the original ausm algorithm developed for high speed applications has been constructed so that the resulting algorithm can be used at all speeds

a nondiffusive finite volume scheme for the three dimensional maxwell s equations on unstructured meshes we prove a sufficient cfl like condition for the l2 stability of the second order accurate finite volume scheme proposed by remaki for the time domain solution of maxwell s equations in heterogeneous media with metallic and absorbing boundary conditions we yield a very general sufficient condition valid for any finite volume partition in two and three space dimensions numerical tests show the potential of this original finite volume scheme in one two and three space dimensions for the numerical solution of maxwell s equations in the time domain

hybrid upwind methods for the simulation of unsteady shock wave diffraction over a cylinder abstract assessment of three hybrid upwind methods in unsteady shock wave diffraction over a cylinder is presented the study includes two hybrid flux vector splitting fvs methods and a hybrid riemann solver the hybrid fvs schemes are constructed by a combination of flux vector splitting and second order artificial dissipation the hybrid fvs riemann solver is constructed by the combination of a characteristic flux averaging method and a fvs scheme the above schemes are implemented in conjunction with an implicit unfactored method computations are performed for unsteady shock diffraction over a cylinder and comparisons are presented with other numerical and experimental results from literature including recent unstructured adaptive grid computations emphasis is given on the accurate prediction of the unsteady pressure loads on the cylinder surface since this is of interest in engineering applications related to explosions and fluid structure interaction

a comparative study of characteristic based algorithms for the maxwell equations characteristic based finite difference and finite volume schemes have been developed for solving the three dimensional maxwell equations in the time domain a detailed eigenvector analysis for the maxwell equations in a general curvilinear coordinate has also been completed to provide a basic framework for future finite difference schemes although the basic concepts of the two algorithms are identical the detailed formulations are vastly different for achieving split flux vectors according to the sign of the eigenvalues a comparative study of these algorithms applied to an oscillating electric dipole is carried out to assess their relative merit for further development in spherical coordinates second order windward numerical simulations of the radiating phenomenon are closely comparable in terms of accuracy and efficiency these methods also demonstrate an ability to suppress reflected waves from the truncated boundary by a simple compatibility condition

on the 3d kelvin voigt brinkman forchheimer equations in some unbounded domains abstract considered here is the first initial boundary value problem for the kelvin voigt brinkman forchheimer equations in three dimensional domains satisfying the poincare inequality the existence of a weak solution to the problem is proved by using the faedo galerkin method then we show the existence of a unique minimal pullback d attractor for the process associated to the problem with respect to a large class of non autonomous forcing terms finally the existence uniqueness and stability of a stationary solution is studied when the external force is time independent and small

effect of the numerical scheme resolution on quasi 2d simulation of an automotive radial turbine under highly pulsating flow automotive turbocharger turbines usually work under pulsating flow because of the sequential nature of engine breathing however existing turbine models are typically based on quasi steady assumptions in this paper a model where the volute is calculated in a quasi 2d scheme is presented the objective of this work is to quantify and analyse the effect of the numerical resolution scheme used in the volute model the conditions imposed upstream are isentropic pressure pulsations with different amplitude and frequency the volute is computed using a finite volume approach considering the tangential and radial velocity components the stator and rotor are assumed to be quasi steady in this paper different integration and spatial reconstruction schemes are explored the spatial reconstruction is based on the muscl method with different slope limiters fulfilling the tvd criterion the model results are assessed against 3d u rans calculations the results show that under low frequency pressure pulses all the schemes lead to similar solutions but for high frequency pulsation the results can be very different depending upon the selected scheme this may have an impact in noise emission predictions

upwind relaxation algorithms for the navier stokes equations analyse des erreurs de troncature de la differenciation spatiale et analyse de la stabilite de l algorithme de relaxation calcul pour une serie d ecoulements a l aide de la forme couche mince des equations calcul du decollement de couche limite induit par chocs

a fractional step method for solving 3d time domain maxwell equations abstract stable and efficient implicit and explicit fractional step methods for solving three dimensional time dependent maxwell equations have been successfully developed these numerical procedures are characteristic based schemes with the intrinsically accurate no reflection wave condition on the boundaries of truncated computational domain excellent simulations tot electromagnetic phenomena have been achieved for a three dimensional wave guide and an oscillating electric dipole

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

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

numerical simulation of dynamic stall using an improved advection upwind splitting method in this study a dual time integration method with the advection upwind splitting method based on flux difference ausmd scheme is demonstrated with simplicity robustness and accuracy in solving the time dependent full navier stoke equations for aerodynamic analysis of stationary and oscillating airfoils a pseudotime is introduced as an iteration strategy so that time accuracy for solving the unsteady equations can be preserved for long time a second order time accurate euler backward implicit discretization is made at the physical time level a two stage runge kutta scheme is used in the pseudotime iteration in combination with acceleration enhancement procedures the local time stepping and residual smoothing the recent ausmd flux scheme with a slight modification is applied for approximating the inviscid terms this modification has been found necessary to provide robust and accurate solutions for the study of dynamic stall meanwhile the renormalization group theory model is chosen to evaluate the turbulence eddy viscosity both light and deep dynamic stall cases were calculated along with grid refinement and time stepping size studies results of unsteady airload hysteresis curves and instantaneous flow pictures are analyzed and compared with measured data

integration by table look up for p version finite elements on curved tetrahedra abstract we develop a method of evaluating element level matrices and vectors associated with p version finite element computations on tetrahedral meshes with curved boundaries the procedure uses optimal interpolation formula q chen i babuska approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle comput methods appl mech engrg 128 1995 405 417 q chen i babuska approximate optimal polynomial interpolation points in the tetrahedron comput methods appl mech engrg 137 1997 89 94 for non polynomial portions of integrands followed by exact integration exact integrals of product combinations of polynomial interpolants and shape functions are stored so that different integrals may be efficiently evaluated by a table look up we present error analysis for our scheme applied to curvilinear tetrahedral meshes with exact geometric representation of the boundary of the domain as defined in a geometric modelling system numerical results are presented for problems involving the helmholtz equation

quadrature free implementation of discontinuous galerkin method for hyperbolic equations a discontinuous galerkin formulation that avoids the use of discrete quadrature formulas is described and applied to linear and nonlinear test problems in one and two space dimensions this approach requires less computational time and storage than conventional implementations but preserves the compactness and robustness inherent in the discontinuous galerkin method test problems include the linear and nonlinear one dimensional scalar advection of smooth initial value problems that are discretized by using unstructured grids with varying degrees of smoothness and regularity and two dimensional linear euler solutions on unstructured grids

computational treatment of source terms in two equation turbulence models the source terms in turbulence models require careful treatment to obtain a stable discretization the choice between implicit and explicit treatment has to be made this can be done either on the basis of individual terms or on the basis of the exact jacobian of the source terms a comparison of both methods shows that the latter is generally applicable and superior to the first approximate method with respect to convergence speed this comes from the possibility of using the multigrid technique with the exact method whereas this is not always possible with the approximate method in principle for robustness a time step restriction for the source terms has to be introduced to prevent the turbulence quantities from becoming negative or infinitely large an approximation of the appropriate time step is calculated practical results however indicate that the time step restriction is not always necessary different two equation turbulence models are investigated confirming the generality of the approach

approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle the main results of this paper are the analysis of the quality of approximation of polynomial interpolation and the computation of the approximate optimal interpolation points in the triangle we introduce various norms for the interpolation operator computational results indicate that for a given polynomial degree the set that minimizes the mean l2 norm of the interpolation operator is close to the smallest lebesgue constant interpolation set in particular for the triangle this set gives the smallest lebesgue constant currently known

on the uniqueness of strong solution to the incompressible navier stokes equations with damping abstract in this paper we show that the cauchy problem of the incompressible navier stokes equations with damping u 1 u 0 has global strong solution for any 3 and the strong solution is unique when 3 5 this improves earlier results

on the existence of explicit hp finite element methods using gauss lobatto integration on the triangle spectral element simulations on quadrilaterals and hexahedra rely on the gauss lobatto gl integration rule to enable explicit simulations with optimal spatial convergence rates in this work it is proved that a similar integration rule does not exist on triangles the following properties of the rule are sought a p 1 p 2 2 point integration rule capable of exactly integrating the space given by cal t 2p 1 equiv x my n 0 leq m n m n leq2p 1 where p is an integer integration points located at each of the triangle vertices p 1 integration points located on each side and p 1 p 2 2 integration points located in the interior of the element the proof hinges on the fact that the existence of such a rule implies the existence of a nodal basis with an approximate diagonal mass matrix that can be inverted to obtain exact galerkin projections of functions in cal t p 1 the proof shows that vertex functions of a basis having this property exist and are unique but on a triangle these functions are not nodal and therefore the gl rule does not exist in spite of this the existence of the vertex functions indicates that there may be a nonnodal basis that has the above property this basis would enable explicit hp finite element simulations on the triangle with optimal spatial accuracy the methodology developed in the paper gives insight into a possible way to find such a basis

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

the equilibrium state method for hyperbolic conservation laws with stiff reaction terms a new fractional step method is proposed for numerical simulations of hyperbolic conservation laws with stiff source terms arising from chemically reactive flows in stiff reaction problems a well known spurious numerical phenomenon the incorrect propagation speed of discontinuities may occur in general fractional step algorithm due to the underresolved numerical solution in both space and time the basic idea of the present proposed scheme is to replace the cell average representation with a two equilibrium states reconstruction during the reaction step which allows us to obtain the correct propagation of discontinuities for stiff reaction problems in an underresolved mesh because the definition of these two equilibrium states for each transition cell is independent of its neighboring cells the proposed method can be extended to multi dimensional problems directly in addition this method is promising to deal with more complicated real world problems after being extended to multi species multi reactions system extensive numerical examples for one and two dimensional scalar and euler system demonstrate the reliability and robustness of this novel method

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

numerical problems in semiconductor simulation using the hydrodynamic model a second order finite difference scheme in this paper a second order total variation diminishing tvd finite difference scheme of upwind type is employed for the numerical approximation of the classical hydrodynamic model for semiconductors proposed by blotekjaer and baccarani wordeman in particular the high order hyperbolic fluxes are evaluated by a suitable extrapolation on adjacent cells of the first order fluxes of roe while total variation diminishing is achieved by limiting the slopes of the discrete riemann invariants using the so called flux corrected transport approach extensive numerical simulations are performed on a submicron n n n ballistic diode the numerical experiments show that the spurious oscillations arising in the electron current are not completely suppressed by the tvd scheme and can lead to serious numerical instabilities when the solution of the hydrodynamic model is non smooth and the computational mesh is coarse the accuracy of the numerical method is investigated in terms of conservation of the steady electron current the obtained results show that the second order scheme does not behave much better than a corresponding first order one due to a poor performance of the slope limiters caused by the presence of local extrema of the riemann invariant associated with the hyperbolic system

navier stokes equations with delays on unbounded domains abstract some results on the existence and uniqueness of solutions to navier stokes equations when the domain is unbounded and the external force contains some hereditary characteristics are proved for both the evolutionary and the stationary cases exponential stability of the stationary solution is also established in dimension two

simultaneous solution algorithms for eulerian eulerian gas solid flow models stability analysis and convergence behaviour of a point and a plane solver simultaneous solution algorithms for eulerian eulerian gas solid flow models are presented and their stability analyzed the integration algorithms are based on dual time stepping with fourth order runge kutta in pseudo time the domain is solved point or plane wise the discretization of the inviscid terms is based on a low mach limit of the multi phase preconditioned advection upstream splitting method mp ausmp the numerical stability of the simultaneous solution algorithms is analyzed in 2d with the fourier method stability results are compared with the convergence behaviour of 3d riser simulations the impact of the grid aspect ratio preconditioning artificial dissipation and the treatment of the source terms is investigated a particular advantage of the simultaneous solution algorithms is that they allow a fully implicit treatment of the source terms which are of crucial importance for the eulerian eulerian gas solid flow models and their solution the numerical stability of the optimal simultaneous solution algorithm is analyzed for different solids volume fractions and gas solid slip velocities furthermore the effect of the grid resolution on the convergence behaviour and the simulation results is investigated finally simulations of the bottom zone of a pilot scale riser with a side solids inlet are experimentally validated

numerical solution of two carrier hydrodynamic semiconductor device equations employing a stabilized finite element method abstract a space time galerkin least squares finite element method was presented in 1 for numerical simulation of single carrier hydrodynamic semiconductor device equations the single carrier hydrodynamic device equations were shown to resemble the ideal gas equations and galerkin least squares finite element method originally developed for computational fluid dynamics equations 16 was extended to solve semiconductor device applications in this paper the space time galerkin least squares finite element method is further extended and generalized to solve two carrier hydrodynamic device equations the proposed formulation is based on a time discontinuous galerkin method in which physical entropy variables are employed a standard galerkin finite element method is applied to the poisson equation numerical simulations are performed on the coupled poisson and the two carrier hydrodynamic equations employing a staggered approach a mathematical analysis of the time dependent multi dimensional hydrodynamic model is performed to determine well posed boundary conditions for electrical contacts the number of boundary conditions that need to be specified for the hydrodynamic equations at inflow and outflow boundaries of the device are derived example boundary conditions that are based either on physical and or mathematical basis are presented stability of the numerical algorithms is addressed the space time galerkin least squares finite element method and the standard galerkin finite element method for the hydrodynamic and poisson equations respectively are shown to be stable specifically a clausius duhem inequality a basic stability requirement is derived for the hydrodynamic equations and the proposed numerical method automatically satisfies this stability requirement numerical simulations are performed on one and two dimensional two carrier p n diodes and the results demonstrate the effectiveness of the proposed numerical method

an extended lagrangian method a unique formulation of describing fluid motion is presented the method referred to as extended lagrangian method is interesting from both theoretical and numerical points of view the formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the eulerian description the present method and the arbitrary lagrangian eulerian ale method have a similarity in spirit eliminating the cross streamline numerical diffusion for this purpose we suggest a simple grid constraint condition and utilize an accurate discretization procedure this grid constraint is only applied to the transverse cell face parallel to the local stream velocity and hence our method for the steady state problems naturally reduces to the streamline curvature method without explicitly solving the steady streamline coordinate equations formulated a priori unlike the lagrangian method proposed by loh and hui which is valid only for steady supersonic flows the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows simply by invoking in the same code an appropriate grid constraint suggested in this paper the approach is found to be robust and stable it automatically adapts to flow features without resorting to clustering thereby maintaining rather uniform grid spacing throughout and large time step moreover the method is shown to resolve multi dimensional discontinuities with a high level of accuracy similar to that found in one dimensional problems

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

geometry representation issues associated with p version finite element computations this paper addresses issues related to accurate geometry representation for p version finite elements on curved three dimensional domains specific options to account for domain geometry information during element level computation are identified accuracy requirements on the geometry related approximations to preserve the optimal rate of finite element error convergence for second order elliptic boundary value problems are given an element geometric mapping scheme based on blending the exact shape of the domain boundary is described that can either be used directly during element integrations or used to construct element level geometric approximations of required accuracy smoothness issues of the rational blends on simplex topologies are discussed and a numerical example based on the solution of poisson s equation in three dimensions is presented to illustrate the impact of the rational blends on the optimal rate of finite element error convergence

a new triangular and tetrahedral basis for high order hp finite element methods in this paper we describe the foundations of a new hierarchical modal basis suitable for high order hp finite element discretizations on unstructured meshes it is based on a generalized tensor product of mixed weight jacobi polynomials the generalized tensor product property leads to a low operation count with the use of sum factorization techniques variable p order expansions in each element are readily implemented which is a crucial property for efficient adaptive discretizations numerical examples demonstrate the exponential convergence for smooth solutions and the ability of this formulation to handle easily very complex two and three dmensional computational domains employing standard meshes

a petrov galerkin finite element method for convection dominated flows an accurate upwinding technique for satisfying the maximum principle abstract in this paper we present a new petrov galerkin method for convection dominated flow problems which is conservative and satisfies the discrete maximum principle this method also possesses no spurious crosswind diffusion and gives very accurate solutions the method is representative of a class of methods which may be described as fixed mesh adaptive

grid adaptation using chimera composite overlapping meshes the objective of this paper is to perform grid adaptation using composite over lapping meshes in regions of large gradient to capture the salient features accurately during computation the chimera grid scheme a multiple overset mesh technique is used in combination with a navier stokes solver the numerical solution is first converged to a steady state based on an initial coarse mesh solution adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high gradient region but without requiring the mesh boundaries to join in any special way communications through boundary interfaces between those separated grids are carried out using tri linear interpolation applications to the euler equations for shock reflections and to a shock wave boundary layer interaction problem are tested with the present method the salient features are well resolved

a fast method of numerical quadrature for p version finite element matrices a new technique of numerical quadrature especially suited for quadrilateral and hexahedron p version finite element matrices is presented this new technique separates the integrand into two parts and numerically operates on each part separately the objective of this scheme is to minimize the computational cost of integrating the entire element matrix as opposed to minimizing the cost of integrating a single function the efficiency of the new technique is compared with gaussian quadrature and found to take a small fraction of the computational effort

godunov type schemes with an inertia term for unsteady full mach number range flow calculations an inertia term is introduced in the ausm up scheme the resulting scheme called ausm it it for inertia term is designed as an extension of the ausm up scheme allowing for full mach number range calculations of unsteady flows including acoustic features in line with the continuous asymptotic analysis the ausm it scheme satisfies the conservation of the discrete linear acoustic energy at first order in the low mach number limit its capability to properly handle low mach number unsteady flows that may include acoustic waves or discontinuities is numerically illustrated the approach for building the ausm it scheme from the ausm up scheme is applicable to any other godunov type scheme

a multigrid semi implicit line method for viscous incompressible and low mach number flows on high aspect ratio grids abstract discretization of viscous incompressible and viscous low mach number flows often leads to a system of equations which is very difficult to solve there are two reasons first the use of high aspect ratio grids results in a very numerically anisotropic behaviour of the diffusive and acoustic terms and second in low mach number flow the ratio of the convective and acoustic eigenvalues of the inviscid system becomes very high we implemented an ausm based discretization method using an explicit third order discretization for the convective part and a line implicit central discretization for the acoustic part and for the diffusive part the lines are chosen in the direction of the grid points with shortest connection the preconditioned semi implicit line method is used in multistage form because of the explicit third order discretization of the convective part multigrid is used as an acceleration technique it is shown that the convergence is very good independent of grid aspect ratio and mach number

finite element method for solving problems with singular solutions abstract numerical treatment of the elliptic boundary value problem with nonsmooth solution by the finite element method is discussed the nonsmoothness could have its origin in the unsmooth boundary or the differential equation this paper which is a survey of the recent results elaborates among others on the method of auxiliary mapping the partition of unity finite element method and the hp version of fem in three dimensions numerical examples illustrate mathematical results an

monomial cubature rules since stroud a compilation a bibliography of references to cubature rules which have appeared since the publication of stroud s book 1971 is presented the standard regions that are treated in this paper are the n cube the n simplex the n sphere and the entire space

numeric treatment of contact discontinuity with multi gases in this paper we work with a finite volume procedure for the computation of the one dimensional euler equations for the treatment of multi gases and the problem of the correct treatment of the discontinuity was more nearly investigated a suggested equation was embedded in the finite volumes context and implemented in our code accordingly and regarded as validated

symmetric gaussian quadrature formulae for tetrahedronal regions abstract quadrature formulae of degrees 2 to 6 are presented for the numerical integration of a function over tetrahedronal regions the formulae presented are of gaussian type and fully symmetric with respect to the four vertices of the tetrahedron

performance of upwind schemes and turbulence models in hypersonic flows an evaluation of three upwind schemes and four turbulence models is presented in order to assess their respective separate and combined performance in complex hypersonic flows with large scale separation the upwind schemes include liou and steffen s advection upstream splitting method ausm flux vector splitting its modification by wada and liou called ausmdv and roe s flux difference splitting turbulent effects were modeled utilizing wilcox s k model with two compressibility corrections by coakley s group the widely popular spalart allmaras and supersonic transport sst models as well as an explicit algebraic reynolds stress model earsm by wallin and johansson using a powerful explicit implicit finite volume computational fluid dynamics code the upwind schemes are first tested on a complex double wedge euler flow configuration a three dimensional corner flow serves as a test case for a laminar navier stokes computation finally ausm schemes are used in combination with several turbulence models in a two dimensional ramp flow and a three dimensional crossing shock interaction results are compared with either experiments or computations by other authors the authors conclusions suggest that the ausmdv is probably the most recommendable scheme for complex hypersonic flows regarding turbulence modeling models with explicit compressibility corrections in this case the k model seem to deliver presently the comparatively best predictions in complex flows particularly in case of separation

a quantum corrected energy transport model for nanoscale semiconductor devices an energy transport model coupled with the density gradient method as quantum mechanical corrections is proposed and numerically investigated this new model is comprehensive in both physical and mathematical aspects it is capable of describing hot electron transport as well as significant quantum mechanical effects for advanced devices with dimensions comparable to the de broglie wave length the model is completely self adjoint for all state variables and hence provides many appealing mathematical features such as global convergence fast iterative solution and highly parallelizable numerical simulations on diode and mosfet with the gate length down to 34 nm using this model have been performed and compared with that using the classical transport model it is shown that the i v characteristics of this short channel device is significantly corrected by the density gradient equations with current drive reduced by up to 60 comparing with that of the classical model along moreover a 2d quantum layer which is only a fraction of the length scale of inversion layer is also effectively captured by this new model with very fine mesh near the interface produced by an adaptive finite element method

analysis and prediction of thin airfoil stall phenomena with hybrid turbulence methodology analysis and prediction of thin airfoil stall phenomena of a naca 64a006 airfoil are numerically investigated using large eddy simulation les reynolds averaged navier stokes rans hybrid methodology with a high order compact differencing scheme subsonic flow of m 0 17 with the high reynolds number of re 5 8 x 10 6 is considered and the angle of attack is varied from 4 0 to 11 0 deg

a finite element formulation for the hydrodynamic semiconductor device equations abstract a new formulation employing the galerkin least squares finite element method is presented for the simulation of the hydrodynamic model of semiconductor devices numerical simulations are performed on the coupled poisson and hydrodynamic equations for one carrier devices the hydrodynamic equations for a single carrier i e for the electrons or holes resemble the compressible navier stokes equations with the addition of highly nonlinear source terms and without the viscous terms the governing equations are nondimensionalized to improve the conditioning on the resulting system of equations and the efficiency of the numerical algorithms furthermore to establish the stability of the discrete solution the system of hydrodynamic equations is symmetrized by considering generalized entropy functions a staggered solution strategy is employed to treat the coupled hydrodynamic and poisson equations numerical results are presented for one dimensional and two dimensional one carrier n n n devices the presence of velocity overshoot has been observed and it is recognized that the heat flux term plays an important role in the simulation of semiconductor devices employing the hydrodynamic model

least squares finite element formulation for hydrodynamic modeling of semiconductor devices a least squares finite element formulation is presented for the hydrodynamic modeling of semiconductor devices the formulation results in a symmetric and positive definite algebraic system its capability of adopting equal order interpolations for all unknown variables makes it simple to formulate and easy to program the semiconductor hydrodynamic equations coupled with the poisson equation are formulated as one unified equation system in this least squares finite element scheme the developed method is examined on 1 d and 2 d deep submicron semiconductor device structures to demonstrate its capability of handling the large gradients of variables and highly nonlinear source terms in the semiconductor hydrodynamic equations

kinetic schemes on staggered grids for barotropic euler models entropy stability analysis we introduce in the one dimensional framework a new scheme of finite volume type for barotropic euler equations the numerical unknowns namely densities and velocities are defined on staggered grids the numerical fluxes are defined by using the framework of kinetic schemes we can consider general convex pressure laws we justify that the density remains non negative and the total physical entropy does not increase under suitable stability conditions performances of the scheme are illustrated through a set of numerical experiments

stabilized 3d finite elements for the numerical solution of the navier stokes equations in semiconductors abstract in this article we deal with the three dimensional numerical simulation of semiconductor devices using the viscous hydrodynamic vhd transport model a reformulation of the vhd system using entropy variables allows to end up with a quasi linear form that is symmetric and for which a stability result in form of clausius duhem inequality is proved to hold the numerical approximation of the vhd model is then performed using a time discontinuous galerkin least squares finite element formulation including a discontinuity shock capturing operator and based on a fully unstructured tetrahedral decomposition of the device domain the approach combines in a unified framework the stability and optimality features of the standard galerkin method with the ability of the scheme in effectively coping with the strong variations attained by the solution throughout the semiconductor device as is demonstrated by numerical results in the simulation of several benchmark problems subject to quite different boundary conditions

explicit time marching methods for the time dependent euler computations four explicit type time marching methods including one proposed by the authors are examined the tvd conditions of this method are analyzed with the linear conservation law as the model equation performance of these methods when applied to the euler equations are numerically tested seven examples are tested the main concern is the performance of the methods when discontinuities with different strengths are encountered when the discontinuity is getting stronger spurious oscillation shows up for three existing methods while the method proposed by the authors always gives the results with satisfaction the effect of the limiter is also investigated to put these methods in the same basis for the comparison the same spatial discretization is used roe s solver is used to evaluate the fluxes at the cell interface spatially second order accuracy is achieved by the muscl reconstruction

a new flux splitting scheme a new flux splitting scheme is proposed the scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of roe s solver in the euler and navier stokes solutions carried out in this study the scheme is robust and converges as fast as the roe splitting we propose an appropriately defined cell face advection mach number using values from the two straddling cells via associated characteristic speeds this interface mach number is then used to determine the upwind extrapolation for the convective quantities accordingly the name of the scheme is coined as the advection upstream splitting method ausm we also introduce a new pressure splitting which is shown to behave successfully yielding much smoother results than other existing pressure splittings of particular interest is the supersonic blunt body problem in which the roe scheme gives anomalous solutions the ausm produces correct solutions without difficulty for a wide range of flow conditions as well as grids

an accurate and robust flux splitting scheme for shock and contact discontinuities a flux splitting scheme ausmdv has been constructed with an aim at removing numerical dissipation of the van leer type flux vector splittings on a contact discontinuity the obtained scheme is also recognized as an improved advection upstream splitting method ausm by liou and steffen the proposed scheme has the following favorable properties accurate and robust resolution for shock and contact steady and moving discontinuities conservation of enthalpy for steady flows algorithmic simplicity and easy extension to general conservation laws such as that for chemically reacting flows a simple shock fix is presented to cure the numerical shock instability associated with the carbuncle phenomenon and an entropy fix to remove an expansion shock or glitch at the sonic point extensive numerical experiments were conducted to validate the proposed scheme for a wide range of problems and the results are compiled for comparison with several recent upwind methods

multigrid and defect correction for the steady navier stokes equations theoretical and experimental convergence results are presented for nonlinear multigrid and iterative defect correction applied to finite volume discretizations of the full steady 2d compressible navier stokes equations iterative defect correction is introduced for circumventing the difficulty in solving navier stokes equations discretized with a second or higher order accurate convective part by fourier analysis applied to a model equation an optimal choice is made for the operator to be inverted in the defect correction iteration as a smoothing technique for the multigrid method collective symmetric point gauss seidel relaxation is applied with as the basic solution technique exact newton iteration applied to a continuously differentiable first order upwind discretization of the full navier stokes equations for non smooth flow problems the convergence results obtained are already competitive with those of well established navier stokes methods for smooth flow problems the present method performs better than any standard method here first order discretization error accuracy is attained in a single multigrid cycle and second order accuracy in only one defect correction cycle the method contributes to the state of the art in efficiently computing compressible viscous flows

finite volume compact schemes on staggered grids compact finite difference schemes have been recently used in several direct numerical simulations of turbulent flows since they can achieve high order accuracy and high resolution without exceedingly increasing the size of the computational stencil the development of compact finite volume schemes is more revolved due to the appearance of surface and volume integrals while pereira et al j comput phys 167 2001 and smirnov et al aiaa paper 2546 2001 focused on collocated grids in this paper we use the staggered grid arrangement compact schemes can be tuned to achieve very high resolution for a given formal order of accuracy we develop and test high resolution schemes by following a procedure proposed by lele j comput phys 103 1992 which to the best of our knowledge has not yet been applied to compact finite volume methods on staggered grids results from several one and two dimensional simulations for the scalar transport and navier stokes equations are presented showing that the proposed method is capable to accurately reproduce complex steady and unsteady flows

an accurate moving boundary formulation in cut cell methods a cut cell method for cartesian meshes to simulate viscous compressible flows with moving boundaries is presented we focus on eliminating unphysical oscillations occurring in cartesian grid methods extended to moving boundary problems in these methods cells either lie completely in the fluid or solid region or are intersected by the boundary for the latter cells the time dependent volume fraction lying in the fluid region can be so small that explicit time integration schemes become unstable and a special treatment of these cells is necessary when the boundary moves a fluid cell may become a cut cell or a solid cell may become a small cell at the next time level this causes an abrupt change in the discretization operator and a suddenly modified truncation error of the numerical scheme this temporally discontinuous alteration is shown to act like an unphysical source term which deteriorates the numerical solution i e it generates unphysical oscillations in the hydrodynamic forces exerted on the moving boundary we develop an accurate moving boundary formulation based on the varying discretization operators yielding a cut cell method which avoids these discontinuities results for canonical two and three dimensional test cases evidence the accuracy and robustness of the newly developed scheme

semiconductor device simulation using a viscous hydrodynamic model abstract in this article we deal with a hydrodynamic model of navier stokes ns type for semiconductors including a physical viscosity in the momentum and energy equations a stabilized finite difference scheme with upwinding based on the characteristic variables is used for the discretization of the ns equations while a mixed finite element scheme is employed for the approximation of the poisson equation a consistency result for the method is established showing that the scheme is first order accurate in both space and time we also perform a stability analysis of the numerical method applied to a linearized incompletely parabolic system in two space dimensions with vanishing viscosity a thorough numerical parametric study as a function of the heat conductivity and of the momentum viscosity is carried out in order to investigate their effect on the development of shocks in both one and two space dimensional devices

a robust low diffusive kinetic scheme for the navier stokes euler equations a new kinetic scheme based on the equilibrium flux method efm and modified using osher intermediate states is proposed this new scheme called efmo combines the robustness of the equilibrium flux method and the accuracy of flux difference splitting schemes the original efm scheme is expressed in terms of simple wave decomposition in which only the linearly degenerate subpath is calculated from osher numerical flux while nonlinear waves are still evaluated from the regular efm splitting owing to its capability of withstanding intense nonlinear waves and yet exactly resolving contact discontinuities efmo is particularly well suited for the resolution of the navier stokes equations as demonstrated by a series of severe test cases including the high speed viscous flow around a cone a shock boundary layer interaction problem a vacuum apparition problem the hypersonic flow around a circular cylinder at mach 100 and the forward facing step at mach 3

a conservative staggered grid chebyshev multidomain method for compressible flows we present a new multidomain spectral collocation method that uses a staggered grid for the solution of compressible flow problems the solution unknowns are defined at the nodes of a gauss quadrature rule the fluxes are evaluated at the nodes of a gauss lobatto rule the method is conservative free stream preserving and exponentially accurate a significant advantage of the method is that subdomain corners are not included in the approximation making solutions in complex geometries easier to compute

an iterative method for adaptive finite element solutions of an energy transport model of semiconductor devices a self adjoint formulation of the energy transport model of semiconductor devices is proposed this new formulation leads to symmetric and monotonic properties of the resulting system of nonlinear algebraic equations from an adaptive finite element approximation of the model a node by node iterative method is then presented for solving the system this is a globally convergent method that does not require the assembly of the global matrix system and full jacobian matrices an adaptive algorithm implementing this method is described in detail to illustrate the main features of this paper namely adaptation node by node calculation and global convergence numerical results of simulations on deep submicron diode and mosfet device structures are given to demonstrate the accuracy and efficiency of the algorithm

a discontinuous wave in cell numerical scheme for hyperbolic conservation laws a new riemann solver scheme for hyperbolic systems is introduced the method consists of a discretization of the initial data into an approximate representation by discrete discontinuous waves instead of calculating an intercell flux based on these waves the discontinuous waves are propagated directly since the sum total of all discontinuous waves represents an extension of the linear riemann problem the solution is determined straightforwardly for nonlinear systems each timestep is considered a separate linear riemann problem and the projected waves are weighted to a background grid this method is strikingly similar to the particle in cell approach except that discontinuous waves are pushed around instead of macroparticles the method is applied to maxwell s equations and the equations of inviscid gasdynamics for linear systems exact solutions can be achieved without dissipation and exact transmissive boundary condition treatments are trivial to implement for inviscid gasdynamics the nonlinear method tended to resolve discontinuities more sharply than the roe hll or hllc methods while requiring only between 30 and 50 of the execution time under identical conditions the approach is also extremely robust as it works for any courant number in the limit that the courant number becomes infinite the nonlinear solution approaches the linearized solution

an efficient conservative cut cell method for rigid bodies interacting with viscous compressible flows a cartesian cut cell method for viscous flows interacting with freely moving boundaries is presented the method enables a sharp resolution of the embedded boundaries and strictly conserves mass momentum and energy a new explicit runge kutta scheme pc rk is introduced by which the overall computational time is reduced by a factor of up to 2 5 the new scheme is a predictor corrector type reformulation of a popular class of runge kutta methods which substantially reduces the computational effort for tracking the moving boundaries and subsequently reinitializing the solver impairing neither stability nor accuracy the structural motion is computed by an implicit scheme with good stability properties due to a strong coupling strategy and the conservative discretization of the flow solver at the material interfaces a new formulation for the treatment of small cut cells is proposed with high accuracy and robustness for arbitrary geometries based on a weighted taylor series approach solved via singular value decomposition the efficiency and the accuracy of the new method are demonstrated for several three dimensional cases of laminar and turbulent particulate flow it is shown that the new method remains fully conservative even for large displacements of the boundaries leading to a fast convergence of the fluid solid coupling while spurious force oscillations inherent to this class of methods are effectively suppressed the results substantiate the good stability and accuracy properties of the scheme even on relatively coarse meshes an efficient cartesian cut cell method for freely moving solid boundaries is presented the new predictor corrector runge kutta scheme pc rk enables simulation speedups of up to 2 5 mass momentum and energy are strictly conserved at the sharply resolved solid fluid interfaces the method exhibits very good stability and accuracy properties even for large displacements of the boundaries spurious force oscillations inherent to this class of methods are suppressed