Multigrid for finite element discretizations of aerodynamics equations

Abstract

A multigrid algorithm for the solution of a finite element stabilized discretization of compressible fluid dynamics equations on unstructured grids is described. The solution of the stationary problems is sought by time-stepping and a linearization of the nonlinear discrete systems leads to a very large system of linear equations. These systems are ill-conditioned and require efficient computational procedures. The numerical experiments for Navier-Stokes and Euler systems are presented. The method can be easily included in a parallel library as a preconditioner.