Higher-Order and Adaptive Discontinuous Galerkin Methods with Shock-Capturing Applied to Transonic Turbulent Delta Wing Flow

Abstract

Discontinuous Galerkin (DG) methods allow high-order flow solutions on unstructured or locally refined meshes by increasing the polynomial degree and using curved instead of straight-sided elements. DG discretizations with higher polynomial degrees must, however, be stabilized in the vicinity of discontinuities of flow solutions like shocks. In this article, we device a consistent shock-capturing method for the RANS-kw turbulence model equations based on an artificial viscosity term that depends on element residual terms. Furthermore, the discontinuous Galerkin method is combined with a residual-based adaptation algorithm that targets at resolving all flow features. The higher-order and adaptive DG method is applied to a fully turbulent transonic flow around the second Vortex Flow Experiment (VFE-2) configuration.