A new finite element formulation for computational fluid dynamics. X - The compressible Euler and Navier-Stokes equations

[1]  S. K. Godunov,et al.  THE PROBLEM OF A GENERALIZED SOLUTION IN THE THEORY OF QUASILINEAR EQUATIONS AND IN GAS DYNAMICS , 1962 .

[2]  J. E. Carter,et al.  Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner , 1972 .

[3]  P. A. Thompson,et al.  Compressible Fluid Dynamics , 1972 .

[4]  S. Jordan,et al.  Oscillatory Drag, Lift, and Torque on a Circular Cylinder in a Uniform Flow , 1972 .

[5]  R. F. Warming,et al.  Diagonalization and simultaneous symmetrization of the gas-dynamic matrices , 1975 .

[6]  R. W. MacCormack,et al.  Numerical Solutions of Supersonic and Hypersonic Laminar Compression Corner Flows , 1976 .

[7]  M. Holden,et al.  A study of flow separation in regions of shock wave-boundary layer interaction in hypersonic flow , 1978 .

[8]  Bertil Gustafsson,et al.  Incompletely parabolic problems in fluid dynamics , 1978 .

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

[10]  T. Hughes,et al.  A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions: application to the streamline-upwind procedure. , 1982 .

[11]  T. R. Hughes,et al.  Mathematical foundations of elasticity , 1982 .

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

[13]  E. Tadmor.  Skew-selfadjoint form for systems of conservation laws , 1984 .

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

[15]  A Petrov-Galerkin finite element method for the compressible Euler and Navier-Stokes equations , 1986 .

[16]  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 .

[17]  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 .

[18]  E. Thornton,et al.  A finite element approach for prediction of aerothermal loads , 1986 .

[19]  A mixed finite element method for boundary flux computation , 1986 .

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

[21]  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 .

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

[23]  T. Hughes,et al.  Finite element method for high-speed flows - Consistent calculation of boundary flux , 1987 .

[24]  Czesław I. Bajer,et al.  Notes on the stability of non‐rectangular space–time finite elements , 1987 .

[25]  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 .

[26]  Thomas J. R. Hughes,et al.  Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations†‡ , 1987 .

[27]  T. Hughes,et al.  Space-time finite element methods for elastodynamics: formulations and error estimates , 1988 .

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

[29]  A. Galeão,et al.  A consistent approximate upwind Petrov—Galerkin method for convection-dominated problems , 1988 .

[30]  P. Dutt,et al.  Stable boundary conditions and difference schemas for Navier-Stokes equations , 1988 .

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

[32]  T. Hughes,et al.  A multi-element group preconditioned GMRES algorithm for nonsymmetric systems arising in finite element analysis , 1989 .

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

[34]  Thomas J. R. Hughes,et al.  Space-time finite element methods for second-order hyperbolic equations , 1990 .

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

[36]  Thomas J. R. Hughes,et al.  A new finite element formulation for computational fluid dynamics: IX. Fourier analysis of space-time Galerkin/least-squares algorithms , 1991 .