An explicit space-time discontinuous Galerkin scheme with local time-stepping for unsteady flows

Abstract

The objective of our project is the development of high-order methods for the unsteady Euler and Navier Stokes equations. For this, we consider an explicit DG scheme formulated in a space-time context called the Space-Time Expansion DG scheme (STE-DG). Our focus lies on the improvement of two main aspects: Increase of efficiency in the temporal and spatial discretization by giving up the assumption that all grid cells run with the same time step and introducing local time-stepping and the shock capturing property, where we have adopted the artificial viscosity approach as described by Persson and Peraire to our STE-DG scheme. Thus, we try to resolve the shock within a few relatively large grid cells forming a narrow viscous profile by locally adding some amount of artificial viscosity. © 2010 Springer-Verlag Berlin Heidelberg.