Grid Adaptation in the Context of DG and FV
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High-fidelity computations are expensive, but required to simulate complex aircraft configurations for all flight regimes. Adaptive methods improve the accuracy-to-effort ratio by concentrating high flow resolution on regions where it is needed. Those are identified by reliable indicators. For instance, this presentation considers a residual-based indicator that accounts for the error on all flow features regardless of their influence on the boundary integral values \cite{Residualbased}. Alternatively, an adjoint-based indicator for discontinuous Galerkin methods is used for goal-oriented adaptive computations. Also, this work presents first extensions of it to the finite volume method. The indicators are applied to subdivide cells of the mesh (hierarchical h-adaptation, using FSAdaptationNG). In case of DG, they also guide local polynomial enrichment (hp-adaptation). This contribution demonstrates superior accuracy for given computational efforts compared to fixed-grid computations.This work features also metric-based mesh adaptation where the metric field is computed from an accurate Hessian of the Mach number, using the optimal metric formulation from the multiscale error estimator theory. This Hessian, that is computed from a Discontinuous Galerkin weak formulation, is then rescaled using state-of-the-art DG error estimators for high-order computations. The methods have been validated and applied to configurations of increasing complexity, using the remesher Tucanos and the flow solver. The results demonstrate similar or superior accuracy compared to a variety of state-of-the art adaptive and non-adaptive flow solvers.
