Semi-implicit time discretization of the discontinuous Galerkin method for the Navier-Stokes equations

Abstract

We deal with the numerical solution of the compressible Navier-Stokes equations with the aid of the discontinuous Galerkin method. The space semi-discretization leads to a stiff system of ordinary differential equations. In order to accelerate a convergence to the steady-state solution we employ the semi-implicit time discretization which leads to the solution of linear algebra system at each time level. We focus on the solution of the arising linear algebra systems and propose a new efficient strategy for the steady-state solutions. The efficiency is demonstrated by a set of numerical experiments. © 2010 Springer-Verlag Berlin Heidelberg.