Multigrid solver algorithms for DG methods and applications to aerodynamic flows

Abstract

In this chapter we collect results obtained within the IDIHOM project on the development of Discontinuous Galerkin (DG) methods and their application to aerodynamic flows. In particular, we present an application of multigrid algorithms to a higher order DG discretization of the Reynolds-averaged Navier–Stokes (RANS) equations in combination with the Spalart-Allmaras as well as the Wilcox-kω turbulence model. Based on either lower order discretizations or agglomerated coarse meshes the resulting solver algorithms are characterized as p-or h-multigrid, respectively. Linear and nonlinear multigrid algorithms are applied to IDIHOM test cases, namely theL1T2 high lift configuration and the deltawing of the second Vortex Flow Experiment (VFE-2) with rounded leading edge. All presented algorithms are compared to a strongly implicit single grid solver in terms of number of nonlinear iterations and computing time. Furthermore, higher order DG methods are combined with adaptive mesh refinement, in particular, with residual-based and adjoint-based mesh refinement. These adaptive methods are applied to a subsonic and transonic flow around the VFE-2 delta wing.