Analysis of a preconditioned GMRES solver for a nonsymmetric SUPG discretization of the compressible Navier-Stokes equations

A preconditioner for a system of linear equations resulting from finite element discretization of the compressible Navier-Stokes equations in conservative variables is presented. This system is nonsymmetric and the construction of a preconditioner is based on a symmetric preconditioner for a symmetric formulation of flows in entropy variables. The algorithm is a modification of a block Jacobi iteration. It is combined with a GMRES procedure resulting in an effective equation solver. The solver is tested on a number of numerical examples.