Discontinuous Galerkin Methods For Compressible Dns

this paper we formulate, implement, and apply a discontinuous Galerkin (DG) method for the simulation of compressible turbulent flows. Discontinuous Galerkin can be thought of as a hybrid of finite-volume and finite-element methods that has a number of potential advantages including: high-order accuracy on unstructured meshes, local hp-refinement, weak imposition of boundary conditions [1], local conservation, and orthogonal hierarchical bases that support multiscale turbulence modeling [2--4]. The interested reader should consult the reviews of Cockburn [5] and Cockburn et al. [6] for a recent update on the status of discontinuous Galerkin. Since the DG method is ideally suited for hyperbolic or nearly hyperbolic systems, we believe that DG may be a particularly attractive method for high-Reynolds-number # Address all correspondence to this autho