Explicit one-step discontinuous Galerkin schemes for unsteady flow simulations

Abstract

In the following, we describe an explicit discontinuous Galerkin scheme for the compressible Navier-Stokes equations. The scheme is of arbitrary order of accuracy by choosing the polynomial degree of the approximation. It is kept very local so that the solution in each cell only depends on the von Neumann neighbors. Apart from the standard DG framework the computational efficiency is increased by the use of a mixed approach using a modal and a nodal set of basis functions. For the approximation of the viscous fluxes an approximation based on local Riemann solutions is used. At the end we show a high order approximation of the unsteady laminar flow over a NACA0012 profile. © 2010 Springer-Verlag Berlin Heidelberg.