A note on the use of symmetric line GaussSeidel for the steady upwind differenced Euler equations
Abstract
Symmetric Line GaussSeidel (SLGS) 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 GaussSeidel 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.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 July 1987
 Bibcode:
 1987STIN...8813540M
 Keywords:

 Compressible Flow;
 Computational Fluid Dynamics;
 Convergence;
 Differential Equations;
 Euler Equations Of Motion;
 Inviscid Flow;
 Relaxation Method (Mathematics);
 Alternating Direction Implicit Methods;
 Computational Grids;
 Fourier Analysis;
 Gas Flow;
 Fluid Mechanics and Heat Transfer