Discontinuous Galerkin Methods for Compressible DNS

A discontinuous Galerkin (DG) method is formulated, implemented, and tested for simulation of compressible turbulent flows. The method is applied to a range of test problems including steady and unsteady flow over a circular cylinder, inviscid flow over an inclined ellipse, and fully developed turbulent flow in a planar channel. In all cases, local hp-refinement is utilized to obtain high quality solutions with fewer degrees of freedom than traditional numerical methods. The formulation and validation cases presented here lay the foundation for future applications of DG for simulation of compressible turbulent flows in complex geometries.