H- and hp-adaptive methods in a unified DG-FV framework using mesh subdivision

Kurzfassung

To simulate complex aircraft configurations high-fidelity computations are needed, that provide accu- rate results for all flight regimes. These computations are computationally very expensive. To reduce computational effort, adaptive simulation techniques can be used, which resolve the flow with high accuracy only in regions where it is needed. To drive such adaptive methods, reliable indicators are needed, which determine the regions of the mesh that need to be refined. We present a Discontinuous Galerkin (DG) method and a finite Volume (FV) method in a unified framework, which allows compu- tations on locally refined non-conforming meshes. In this framework, two indicators are derived. The first indicator considered is the residual-based indicator, which will resolve all flow features regardless of their influence on the boundary integral values. As a second indicator, the adjoint-based indicator for DG methods is used for goal-oriented adaptive computations. For FV methods first extensions of goal-oriented indicators are presented. The previous indicators are combined with local polynomial enrichment and mesh subdivision for DG methods in the form of hp-adaptive methods and with mesh subdivision (h-adaptive) for FV methods. These h- and hp-adaptive methods are demonstrated for several aerodynamic test cases and show superior accuracy per number of degrees of freedom as well as superior accuracy for a given computational effort compared to fixed-grid computations. This work has been conducted and implemented in the CFD software by ONERA, DLR and Airbus (CODA). CODA is the computational fluid dynamics (CFD) software being developed as part of a collaboration between the French Aerospace Lab ONERA, the German Aerospace Center (DLR), Airbus, and their European research partners. CODA is jointly owned by ONERA, DLR and Airbus.