A hybrid mixed method for the compressible Navier-Stokes equations

We present a novel discretization method for nonlinear convection-diffusion equations and, in particular, for the compressible Navier-Stokes equations. The method is based on a Discontinuous Galerkin (DG) discretization for convection terms, and a Mixed method using H(div) spaces for the diffusive terms. Furthermore, hybridization is used to reduce the number of globally coupled degrees of freedom. For the scalar case, a local postprocessing procedure is used to enhance the quality of the approximate solution wh. The method reduces to a DG scheme for pure convection, and to a Mixed method for pure diffusion, while for the intermediate case the combined variational formulation requires no additional parameters. We formulate and validate our scheme for nonlinear model problems, as well as compressible flow problems.