A Genuinely Multidimensional Upwind Scheme and Efficient Multigrid Solver for the Compressible Euler Equations.

Abstract

We present a new approach towards the construction of a genuinely multidimensional high-resolution scheme for computing steady-state solutions of the Euler equations of gas dynamics. The unique advantage of this approach is that the Gauss-Seidel relaxation is stable when applied directly to the high-resolution discrete equations, thus allowing us to construct a very efficient and simple multigrid steady-state solver. This is the only high-resolution scheme known to us that has this property. The two-dimensional scheme is presented in detail. It is formulated on triangular (structured and unstructured) meshes and can be interpreted as a genuinely two-dimensional extension of the Roe scheme. The quality of the solutions obtained using this scheme and the performance of the multigrid algorithm are illustrated by the numerical experiments. Construction of the three dimensional scheme is outlined briefly as well. (AN)

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1994
Accession Number
ADA289712

Entities

People

  • David Sidilkover

Tags

DTIC Thesaurus Topics

  • Compressible Flow
  • Computational Fluid Dynamics
  • Computational Science
  • Coordinate Systems
  • Differential Equations
  • Equations
  • Euler Equations
  • Fluid Dynamics
  • Fluid Flow
  • Gas Dynamics
  • High Resolution
  • Incompressible Flow
  • Navier Stokes Equations
  • Steady State
  • Three Dimensional
  • Turbulent Mixing
  • Two Dimensional

Readers

  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)