Discontinuous Galerkin Method on unstructured hexahedral grids for 3D Euler and Navier-Stokes Equations

*, † ‡ A Finite-Element Discontinuous Galerkin Method (DGM) has been developed for the 3D Euler and Navier-Stokes equations on unstructured hexahedral grids. Specific features of high order DGM on these grids are described including the implementation of a p-multigrid convergence acceleration method, associated to an agglomeration based h-multigrid approach. The algorithm has been validated and evaluated in terms of accuracy, CPU time and memory performance on a variety of test cases (not all being presented in this paper) such as the inviscid flow around a cylinder, a laminar flat plate, laminar flow over a cylinder, the 3D Poiseuille flow, as well as a representative aero-acoustic test case for the linearized Euler approximation of the propagation of a 3D acoustic wave. An application of the DGM is presented for a 3D turbulent flow over an isolated wing where the results are compared with a standard second-order finite volume method.