A Three-Dimensional Recovery-Based Discontinuous Galerkin Method for Turbulence Simulations

Abstract

Discontinuous Galerkin (DG) methods have recently received much attention because of their portability to complex geometries, scalability in parallel architectures and relatively simple extension to high order. However, their implementation for compressible turbulence problems is not straightforward, e.g., due to parameter-free limiting for orders greater than first and the lack of a consistent high-order diffusion scheme for DG. To address this last point, Van Leer proposed the idea of recovery-based discontinuous Galerkin (RDG) approaches. In the present work, an explicit recovery-based diffusion scheme is developed in three dimensions on a Cartesian grid to solve incompressible and slightly compressible turbulence problems. It is shown that the selection of an optimal recovery and enhancement basis preserves the super-convergence property of this scheme (eighth order for P = 2, where P is the order of the polynomial basis) for the three-dimensional Navier-Stokes equations. Test problems confirm the efficient and accurate application of the present recovery-based discontinuous Galerkin method to incompressible and slightly compressible turbulence problems. I.