Cavity Simulations Using an Explicit Discontinuous Galerkin Scheme with Local Time-Stepping

Abstract

The objective of our project is the development of high-order methods for the unsteady Navier-Stokes equations and their application to cavity flow by means of Large-Eddy-Simulation (LES). For this purpose, we consider discontinuous Galerkin schemes. These methods bear the potential to solve CFD problems for aerospace applications more efficiently, by making use of three different advantages: High order accuracy, complex geometries due to the fact that they can cope with unstructured meshes and adaptivity in polynomial degree as well as mesh refinement (P-, h- and hP-adaptation).

Our explicit DG scheme is called the Space-Time Expansion DG scheme (STEDG) and is formulated in a space-time context. In our current approach towards LES, the key idea is to have a local resolution based indicator, which measures the resolution quality within each grid cell. If under-resolution is detected, a cell-wise constant artificial viscosity is determined for an additional Laplacian diffusion term, which acts as an overall stabilization of the computation. In the context of LES modelling, the proposed approach can be classified as Implicit LES (ILES).