High-order unstructured grid generation and Discontinuous Galerkin discretization applied to a 3D high-lift configuration

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. However, one of the currently largest obstacles to applying these methods to aerodynamic configurations of medium to high complexity is the availability of appropriate higher order curved meshes.

In this article, we describe a complete chain of higher order unstructured grid generation and higher order Discontinuous Galerkin flow solution applied to a turbulent flow around a 3D high-lift configuration. This includes (i) the generation of an appropriately coarse straight-sided mesh, (ii) the evaluation of additional points on the CAD geometry of the curved wall boundary for defining a piecewise polynomial boundary representation, (iii) a higher order mesh deformation to translate the curvature from the wall boundary into the interior of the computational domain, and (iv) the description of a Discontinuous Galerkin discretization which is sufficiently stable to allow a flow computation on the resulting curved mesh. Finally, a fourth order flow solution of the RANS and k-omega turbulence model equations computed on a fourth order unstructured hybrid mesh around a 3D high-lift configuration will be compared against wind-tunnel measurements of the SWING project.