Discontinuous Galerkin schemes for the compressible Navier-Stokes equations

The discretization of the viscous terms in a space discontinuous Galerkin method is investigated through a theoretical analysis and numerical calculations. Two formulations are considered : the first one uses a shifted cell and the other one auxiliary variables. Both are second order accurate on Cartesian meshes. They are applied to the interaction of a reflected shock with a boundary layer in a shock tube and compared to a higher order TVD scheme. Discontinuous Galerkin methods are found to provide accurate solutions for the unsteady compressible Navier-Stokes equations.