Efficient solution strategy for the semi-implicit discontinuous Galerkin discretization of the Navier-Stokes equations

Abstract

The paper deals with the numerical solution of the system of the compressible Navier-Stokes equations with the aid of the interior penalty Galerkin method. We employ a semi-implicit time discretization which leads to the solution of a sequence of linear algebraic systems.

We develop an efficient strategy for the solution of these systems. The presented numerical experiments show that the proposed strategy is efficient for steady-state problems using various grids, polynomial degrees of approximations and flow regimes.

Finally, we apply this strategy with a minor modification to an unsteady flow.

Keywords

• efficient solution strategy
• semi-implicit discontinuous Galerkin discretization
• Navier-Stokes equations