A Note on the Use of Symmetric Line Gauss-Seidel for the Steady Upwind Differenced Euler Equations,

Abstract

Symmetric Line Gauss-Seidel relaxation, when used to compute steady solutions to the upwind differences Euler equations of gas dynamics, is shown to be unstable. The instability occurs for the long waves. If SLGS is used in a multigrid scheme, stability is restored. However, the use of an unstable relaxation scheme will not provide a robust multigrid code. Damped Symmetric Point Gauss-Seidel relaxation is stable and provides similar multigrid convergence rates at much lower cost. However, it fails if the flow is aligned with the grid over a substantial part of the computational domain. Damped Alternating Direction Line Jacobi relaxation can overcome this problem.

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Document Details

Document Type
Technical Report
Publication Date
Jul 29, 1987
Accession Number
ADA185223

Entities

People

  • William A. Mulder

Organizations

  • Stanford University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Amplification
  • Boundaries
  • Computer Science
  • Convergence
  • Differential Equations
  • Equations
  • Euler Equations
  • Flow
  • Free Stream
  • Instability
  • Mathematics
  • Military Research
  • Navier Stokes Equations
  • Residuals
  • Steady State
  • Universities

Fields of Study

  • Mathematics
  • Physics

Readers

  • Control Systems Engineering.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)