Assessment of a high-order discontinuous Galerkin method for vortex convection and wave propagation on unstructured meshes

Abstract

A high-order accurate flow solver based on a discontinuous Galerkin method has been developed for the numerical simulation of vortex convection and wave propagation on unstructured meshes. To assess the performance of the present flow solver, a vortex convection problem in freestream and an acoustic benchmark problem were tested. An airfoil-vortex interaction problem was also simulated by coupling the flow solver with a dynamic mesh adaptation technique. From the mesh resolution test, the present fourth-order discontinuous Galerkin method almost perfectly preserves the vortex and also accurately resolves the acoustic waves on a mesh with an element size of half of characteristic length. It was also observed that the fourth-order method is more than ten times efficient, in terms of the number of degrees of freedom and the elapsed CPU time, compared to the second-order method.