High-order discontinuous Galerkin method for computation of turbulent flows

This paper presents a high-order discontinuous Galerkin method for computation of compressible turbulent flows in three space dimensions. A modified Spalart-and-Allmaras turbulence model is implemented and discretized to the same order of accuracy as that for the Reynolds-averaged Navier-Stokes equations. The creation of curvilinear meshes for arbitrary three-dimensional configurations is achieved through the aid of a computational analysis programming interface, which enables direct communications with the computer-aided design module to determine the true positions of surface quadrature points for high-order geometric representations. A modified linear elasticity approach is used sequentially and is of crucial importance for reshaping the interior mesh to allow high-aspect-ratio curved elements in turbulent boundary layers. Requirements of the mesh parameters, including the wall spacing and viscous stretching factor, are studied; and it is concluded that, for attached turbulent flows, the conventional settings often used in low-order methods should be less stringent when a higher-order method is considered. Several other numerical examples, including a direct numerical simulation of the Taylor-Green vortex and turbulent flow over an ONERA M6 wing, are considered to assess the solution accuracy and to demonstrate the performance of high-order discontinuous Galerkin methods in capturing transitional and turbulent flow phenomena.