Multigrid solution of the steady Euler equations
Abstract
A multigrid (MG) method for the approximation of steady solutions to the full twodimensional Euler equations is described. The space discretization is obtained by the finite volume technique and Osher's approximate Riemannsolver. Symmetric GaussSeidel relaxation is applied to solve the nonlinear discrete system of equations. A multigrid method, the full approximation scheme, accelerates this iterative process. In twodimensional test problems, (subsonic, transonic and supersonic) the multigrid iteration is applied to an initial estimate obtained by the FMGtechnique (nested iteration). For the discretization on the different levels, a fully consistent sequence of nested discretizations is used. The prolongations and restrictions selected agree with this consistency. It turns out that the total amount of work required to obtain a solution that is accurate up to truncation error, corresponds to a small number of nonlinear GaussSeidel iterations. In transonic flow the rate of convergence of the MGiteration appears independent of the number of cells in the discretization.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 May 1985
 Bibcode:
 1985STIN...8617696H
 Keywords:

 Computational Fluid Dynamics;
 Euler Equations Of Motion;
 Iterative Solution;
 Discrete Functions;
 Linearization;
 Subsonic Flow;
 Supersonic Flow;
 Transonic Flow;
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer