Generation of unstructured curvilinear grids and high-order discontinuous Galerkin discretization applied to a 3D high-lift configuration

Summary 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 DG flow solution applied to a turbulent flow around a three‐dimensional high‐lift configuration. This includes (i) the generation of an appropriately coarse straight‐sided mesh; (ii) the evaluation of additional points on the computer‐aided design 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 DG discretization, which is sufficiently stable to allow a flow computation on the resulting curved mesh. Finally, a fourth‐order flow solution of the Reynolds‐averaged Navier–Stokes and k‐ω turbulence model equations is computed on a fourth‐order unstructured hybrid mesh around the three‐dimensional high‐lift simulation of wing‐flow noise generation configuration. Copyright © 2016 John Wiley & Sons, Ltd. This paper includes a description of a complete chain of unstructured curvilinear grid generation and higher order Discontinuous Galerkin flow solution applied to a turbulent flow around a 3D high‐lift configuration. A fourth order flow solution of the RANS and k‐w turbulence model equations is computed on a fourth order unstructured hybrid (mixed‐element) mesh around the 3D high‐lift SWING configuration. A highly resolved flow solution is obtained featuring a complex vortex system.