P-Anisotropic H-Isotropic adaptive discontinuous Galerkin methods for turbulent flows

Abstract

High-Reynolds number flows feature highly anisotropic regions. To allow for adaptive methods that can efficiently resolve these regions, anisotropic strategies are needed. Furthermore, previous results have shown that purely p-adaptive methods as well as purely h-adaptive methods have severe shortcomings in their applicability and that combined hp-adaptive methods offer superior performance. In this work, an h-adaptive framework using isotropic mesh subdivision is utilized, the anisotropic adaptation is handled by the anisotropic p-enrichement. For this, a modal DG basis in physical space is used. To allow for anisotropic adaptation, a subspace of the full polynomial space is chosen individually for each element. To select candidate elements for refinement a residual-based indicator is used. The anisotropic p-adaptivity is driven by a least-squares reconstruction based competitive refinement technique. The combination of this anisotropic p-adaptivity with h-adaptivity provides better accuracy per degree of freedom compared to a second order h-adaptive method as well as an isotropic hp-adaptive method. The work was carried out in the CFD software by ONERA, DLR and Airbus (CODA).