Stabilized Methods for Compressible Flows

This article reviews 25 years of research of the authors and their collaborators on stabilized methods for compressible flow computations. An historical perspective is adopted to document the main advances from the initial developments to modern approaches.

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[5]  Tayfun E. Tezduyar,et al.  SUPG finite element computation of compressible flows with the entropy and conservation variables formulations , 1993 .

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[12]  Thomas J. R. Hughes,et al.  Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations , 1983 .

[13]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems , 1987 .

[14]  Venkat Venkatakrishnan,et al.  Higher Order Schemes for the Compressible Navier-Stokes Equations , 2003 .

[15]  Tayfun E. Tezduyar,et al.  Parallel computation of unsteady compressible flows with the EDICT , 1999 .

[16]  Tayfun E. Tezduyar,et al.  Finite Element Methods for Fluid Dynamics with Moving Boundaries and Interfaces , 2004 .

[17]  Tayfun E. Tezduyar,et al.  CALCULATION OF THE STABILIZATION PARAMETERS IN FINITE ELEMENT FORMULATIONS OF FLOW PROB- LEMS , 2005 .

[18]  T. Tezduyar,et al.  Improved Discontinuity-capturing Finite Element Techniques for Reaction Effects in Turbulence Computation , 2006 .

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[21]  T. Hughes,et al.  Multiphysics simulation of flow-induced vibrations and aeroelasticity on parallel computing platforms , 1999 .

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[25]  Lihong,et al.  DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR A FORWARD-BACKWARD HEAT EQUATION , 2005 .

[26]  Tayfun E. Tezduyar,et al.  Finite element stabilization parameters computed from element matrices and vectors , 2000 .

[27]  Tayfun E. Tezduyar,et al.  Finite element computation of compressible flows with the SUPG formulation , 1991 .

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[29]  Tayfun E. Tezduyar,et al.  A unified finite element formulation for compressible and incompressible flows using augmented conservation variables , 1998 .

[30]  Thomas J. R. Hughes,et al.  A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems , 1986 .

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[33]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: II. Beyond SUPG , 1986 .

[34]  Tayfun E. Tezduyar,et al.  SUPG finite element computation of viscous compressible flows based on the conservation and entropy variables formulations , 1993 .

[35]  A. Harten.  On the symmetric form of systems of conservation laws with entropy , 1983 .

[36]  G. Hulbert,et al.  A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method , 2000 .

[37]  Guillermo Hauke,et al.  a Unified Approach to Compressible and Incompressible Flows and a New Entropy-Consistent Formulation of the K - Model. , 1994 .

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[39]  Guillermo Hauke.  A Unified Approach to Compressible and Incompressible Flows and a New Entropy-Consistent Formulation of the K-Epsilon Model. , 1995 .

[40]  Tayfun E. Tezduyar,et al.  Stabilization and shock-capturing parameters in SUPG formulation of compressible flows , 2004 .

[41]  Guillermo Hauke,et al.  Simple stabilizing matrices for the computation of compressible flows in primitive variables , 2001 .

[42]  T. Tezduyar.  Computation of moving boundaries and interfaces and stabilization parameters , 2003 .

[43]  Peter Hansbo,et al.  On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws , 1990 .

[44]  Arif Masud,et al.  Effects of Mesh Motion on the Stability and Convergence of ALE Based Formulations for Moving Boundary Flows , 2006 .

[45]  Alessandro Corsini,et al.  A variational multiscale higher-order finite element formulation for turbomachinery flow computations , 2005 .

[46]  Thomas J. R. Hughes,et al.  Scalability of finite element applications on distributed-memory parallel computers , 1994 .

[47]  Thomas J. R. Hughes,et al.  A consistent equilibrium chemistry algorithm for hypersonic flows , 1994 .

[48]  Guglielmo Scovazzi,et al.  A discourse on Galilean invariance, SUPG stabilization, and the variational multiscale framework , 2007 .

[49]  Thomas J. R. Hughes,et al.  A data parallel finite element method for computational fluid dynamics on the Connection Machine system , 1992 .

[50]  Tayfun E. Tezduyar,et al.  Finite element solution of flow problems with mixed-time integration , 1991 .

[51]  Thomas J. R. Hughes,et al.  A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems , 1986 .

[52]  K. Jansen.  A stabilized finite element method for computing turbulence , 1999 .

[53]  Thomas J. R. Hughes,et al.  Multiscale and Stabilized Methods , 2007 .

[54]  Anders Szepessy,et al.  Convergence of a shock-capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions , 1989 .

[55]  Claes Johnson,et al.  Discontinuous Galerkin finite element methods for second order hyperbolic problems , 1993 .

[56]  Guglielmo Scovazzi,et al.  Galilean invariance and stabilized methods for compressible flows , 2007 .

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[58]  Peter Monk,et al.  Continuous finite elements in space and time for the heat equation , 1989 .

[59]  Donald A. French,et al.  Long-time behaviour of arbitrary order continuous time Galerkin schemes for some one-dimensional phase transition problems , 1994 .

[60]  T. Hughes,et al.  The Galerkin/least-squares method for advective-diffusive equations , 1988 .

[61]  T. Hughes,et al.  Stabilized finite element methods. I: Application to the advective-diffusive model , 1992 .

[62]  Claes Johnson,et al.  On the convergence of a finite element method for a nonlinear hyperbolic conservation law , 1987 .

[63]  Thomas J. R. Hughes,et al.  A comparative study of different sets of variables for solving compressible and incompressible flows , 1998 .

[64]  D. Estep,et al.  Global error control for the continuous Galerkin finite element method for ordinary differential equations , 1994 .

[65]  Thomas J. R. Hughes,et al.  Large eddy simulation of turbulent channel flows by the variational multiscale method , 2001 .

[66]  Thomas J. R. Hughes,et al.  Automotive design applications of fluid flow simulation on parallel computing platforms , 2000 .

[67]  T. Tezduyar,et al.  Computation of inviscid compressible flows with the V‐SGS stabilization and YZβ shock‐capturing , 2007 .

[68]  Alessandro Corsini,et al.  Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD) , 2007 .

[69]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier—Stokes equations and the second law of thermodynamics , 1986 .

[70]  S. Dey,et al.  Hierarchical basis for stabilized finite element methods for compressible flows , 2003 .

[71]  Thomas J. R. Hughes,et al.  An efficient communications strategy for finite element methods on the Connection Machine CM-5 system , 1994 .

[72]  Thomas J. R. Hughes,et al.  The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence , 2001 .

[73]  Pierre Jamet.  Stability and Convergence of a Generalized Crank-Nicolson Scheme on a Variable Mesh for the Heat Equation , 1980 .

[74]  Marek Behr,et al.  Parallel finite-element computation of 3D flows , 1993, Computer.

[75]  Masahisa Tabata,et al.  SYMMETRIC FINITE ELEMENT APPROXIMATION FOR CONVECTION-DIFFUSION PROBLEMS. , 1985 .

[76]  Thomas J. R. Hughes,et al.  Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations , 1984 .

[77]  T. Hughes,et al.  The variational multiscale method—a paradigm for computational mechanics , 1998 .

[78]  A. R. Mitchell,et al.  Product Approximation for Non-linear Problems in the Finite Element Method , 1981 .

[79]  Donald A. French,et al.  A continuous space-time finite element method for the wave equation , 1996, Math. Comput..

[80]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[81]  Franco Rispoli,et al.  A stabilized finite element method based on SGS models for compressible flows , 2006 .

[82]  Tayfun E. Tezduyar,et al.  Massively parallel finite element simulation Of compressible and incompressible flows , 1994 .

[83]  David L. Darmofal,et al.  The solution of the compressible Euler equations at low Mach numbers using a stabilized finite element algorithm , 2001 .

[84]  Claes Johnson,et al.  Finite element methods for linear hyperbolic problems , 1984 .

[85]  S. Mittal,et al.  A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. II: Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders , 1992 .

[86]  Masahisa Tabata.  Uniform convergence of the upwind finite element approximation for semilinear parabolic problems , 1978 .

[87]  B. Hulme.  Discrete Galerkin and related one-step methods for ordinary differential equations , 1972 .

[88]  Tayfun E. Tezduyar,et al.  Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations , 1986 .

[89]  Tayfun E. Tezduyar,et al.  Computation of Inviscid Supersonic Flows Around Cylinders and Spheres with the SUPG Formulation and YZβ Shock-Capturing , 2006 .

[90]  M. Mock,et al.  Systems of conservation laws of mixed type , 1980 .

[91]  T. Hughes.  Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods , 1995 .

[92]  Thomas J. R. Hughes,et al.  Stabilized shock hydrodynamics: I. A Lagrangian method , 2007 .

[93]  Thomas J. R. Hughes,et al.  Implementation of a one-equation turbulence model within a stabilized finite element formulation of a symmetric advective-diffusive system☆ , 1993 .

[94]  Tayfun E. Tezduyar,et al.  SUPG finite element computation of inviscid supersonic flows with YZβ shock-Capturing , 2007 .