High-order discontinuous Galerkin solutions of three-dimensional incompressible RANS equations

This paper presents the latest developments of the artificial compressibility flux Discontinuous Galerkin (DG) method introduced in [1], extended in [2] to natural convection flows, in [3] to unsteady flows and, more recently, in [4] to turbulent flows. Here we consider the three-dimensional incompressible Reynolds Averaged Navier-Stokes equations (RANS) coupled with the Spalart-Allmaras (SA) turbulence model.The development of efficient high-order RANS solvers is still a difficult task due to the extreme stiffness of the governing equations. For this reason the turbulence model here has been suitably modified, in the source terms and in the diffusion coefficient, in order to prevent unphysical conditions of the turbulent working variable and of one of the closure functions, which sometimes result in numerical instabilities. The reliability, accuracy and robustness of the method were assessed by computing several test cases in simple and real-life configurations: the flow over a sinusoidal bump, the flow field past a sphere in the supercritical regime, the flow field past a delta wing, and the flow around the DLR-F6 wing body transport configuration.