Multiple grid and Osher's scheme for the efficient solution of the steady Euler equations
Abstract
An iterative method is developed for the solution of the steady Euler equations for inviscid flow. The system of hyperbolic conservation laws is discretized by a finitevolume Osherdiscretization. The iterative method is a multiple grid (FAS) iteration with symmetric GaussSeidel (SGS) as a relaxation method. Initial estimates are obtained by full multigrid (FMG). In the pointwise relaxation the equations are kept in blockcoupled form and local linearization of the equations and the boundary conditions is considered. The efficient formulation of Osher's discretization of the twodimensional nonisentropic steady Euler equations and its linearization is presented. The efficiency of FASSGS iteration is shown for a transonic model problem. It appears that, for the problem considered, the rate of convergence is almost independent of the gridsize and that for all meshsizes the discrete system is solved up to truncation error accuracy in only a few (2 or 3) iteration cycles.
 Publication:

Applied Numerical Mathematics
 Pub Date:
 December 1986
 Bibcode:
 1986ApNM....2..475H
 Keywords:

 Computational Fluid Dynamics;
 Computational Grids;
 Euler Equations Of Motion;
 Flow Equations;
 Steady Flow;
 Inviscid Flow;
 Iterative Solution;
 Pressure Distribution;
 Relaxation Method (Mathematics);
 Transonic Flow;
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer