A high-order h-adaptive discontinuous Galerkin method for unstructured grids based on a posteriori error estimation.

View Video Presentation: https://doi.org/10.2514/6.2021-1696.vid In this paper, we present a mesh h-adaptation strategy suited for the discontinuous Galerkin formulation of the compressible Navier-Stokes equations on unstructured grids, based on the simplicial remeshing library MMG. A novel a posteriori error estimator, combining the measure of the energy associated with the highest-order modes and the inter-element jumps, is used to build the metric field. The performance of the developed mesh adaptation algorithm is assessed for steady laminar viscous flows past a square cylinder and past a NACA0012 airfoil, and for the unsteady laminar viscous flow past a circular cylinder. The gain in accuracy for a given number of degrees of freedom (DoFs) is demonstrated for p=1, p=2 and p=3 polynomial degrees, with respect to uniformly refined simulations.

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