A parallel, high-order discontinuous Galerkin code for laminar and turbulent flows

Abstract In this study we present a solution method for the compressible Navier–Stokes equations as well as the Reynolds-averaged Navier–Stokes equations (RANS) based on a discontinuous Galerkin (DG) space discretisation. For the turbulent computations we use the standard Wilcox k – ω or the Spalart–Allmaras model in order to close the RANS system. We currently apply either a local discontinuous Galerkin (LDG) or one of the Bassi–Rebay formulations (BR2) for the discretisation of second-order viscous terms. Both approaches (LDG and BR2) can be advanced explicitly as well as implicitly in time by classical integration methods. The boundary is approximated in a continously differentiable fashion by curved elements not to spoil the high-order of accuracy in the interior of the flow field. Computations are performed for the circular cylinder, the flat plate and classical airfoil sections like NACA0012. We compare our obtained results with experimental and computational data as well as analytical (boundary layer) predictions for the flat plate. The excellent parallelisation characteristics of the scheme are demonstrated, achieved by hiding communication latency behind computation.