Modern shock-capturing schemes

This paper discusses some of the strategies employed for shock-capturing calculations, especially of highly compressible transient flows. In most such cases, the cost of achieving given resolution can be reduced by an order of magnitude or more by employing a grid that adapts dynamically to the evolving solution. Such a grid implies a need for data structures that are not of the simple matrix type. Advantages and disadvantages of unstructured and partly structured meshes are discussed, as well as some of the requirements for flow algorithms able to perform well on such grids.

[1]  S. Zalesak.  Fully multidimensional flux-corrected transport algorithms for fluids , 1979 .

[2]  P. Roe,et al.  On Godunov-type methods near low densities , 1991 .

[3]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[4]  S. Osher,et al.  Triangle based adaptive stencils for the solution of hyperbolic conservation laws , 1992 .

[5]  J. J. Quirk,et al.  An adaptive grid algorithm for computational shock hydrodynamics , 1991 .

[6]  Philip L. Roe,et al.  Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics , 1986 .

[7]  D. Kontinos,et al.  An explicit, rotated upwind algorithm for solution of the Euler/Navier-Stokes equations , 1991 .

[8]  John Francis Dannenhoffer,et al.  Grid adaptation for complex two-dimensional transonic flows , 1987 .

[9]  Philip L. Roe,et al.  Effect of a multi-dimensional flux function on the monotonicity of Euler and Navier-Stokes computations , 1991 .

[10]  M. Liou,et al.  A New Flux Splitting Scheme , 1993 .

[11]  J. Donea.  A Taylor–Galerkin method for convective transport problems , 1983 .

[12]  W. K. Anderson,et al.  Grid convergence for adaptive methods , 1991 .

[13]  Philip L. Roe,et al.  Discontinuous solutions to hyperbolic systems under operator splitting , 1987 .

[14]  Ijaz Parpia,et al.  Grid restructuring for moving boundaries , 1991 .

[15]  T. J. Barth,et al.  On unstructured grids and solvers , 1990 .

[16]  Bram van Leer,et al.  An Implementation of a Grid-Independent Upwind Scheme for the Euler Equations , 1989 .

[17]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .

[18]  Rainald Löhner,et al.  Some useful data structures for the generation of unstructured grids , 1988 .

[19]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[20]  M. Berger,et al.  Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .

[21]  Herman Deconinck,et al.  Investigation of Roe's 2D wave decomposition models for the Euler equations , 1990 .

[22]  Kenneth G. Powell,et al.  An adaptively-refined Cartesian mesh solver for the Euler equations , 1991 .

[23]  Rainald Loehner,et al.  Generation of unstructured grids and Euler solutions for complex geometries , 1989 .

[24]  G. D. van Albada,et al.  A comparative study of computational methods in cosmic gas dynamics , 1982 .

[25]  Samuel Rippa,et al.  Minimal roughness property of the Delaunay triangulation , 1990, Comput. Aided Geom. Des..

[26]  S. Rippa,et al.  Data Dependent Triangulations for Piecewise Linear Interpolation , 1990 .

[27]  Marcel Vinokur,et al.  Generalized Flux-Vector splitting and Roe average for an equilibrium real gas , 1990 .

[28]  B. Larrouturou.  How to preserve the mass fractions positivity when computing compressible multi-component flows , 1991 .

[29]  A. Wathen.  Realistic Eigenvalue Bounds for the Galerkin Mass Matrix , 1987 .

[30]  Bernard Grossman,et al.  A rotated upwind scheme for the Euler equations , 1991 .

[31]  O. C. Zienkiewicz,et al.  Adaptive remeshing for compressible flow computations , 1987 .

[32]  Clinton P. T. Groth,et al.  Assessment of Riemann solvers for unsteady one-dimensional inviscid flows for perfect gases , 1988 .

[33]  Ijaz H. Parpia.  A planar oblique wave model for the Euler equations , 1991 .

[34]  Jack Hase,et al.  A Delaunay triangulation method and Euler solver for bodies in relative motion , 1991 .

[35]  Rainald Löhner,et al.  Numerical Simulation of Shock Interaction With a Modern Main Battlefield Tank , 1991 .

[36]  Nathan Maman,et al.  On the use of dynamical finite-element mesh adaptation for 2D Simulation of unsteady flame propagation , 1990 .