Unstructured h- and hp-adaptive strategies for discontinuous Galerkin methods based on a posteriori error estimation for compressible flows. (30th January 2022) - Basile, Francesca; Chapelier, Jean-Baptiste; de la Llave Plata, Marta; Laraufie, Romain; Frey, Pascal
Abstract: In this paper, we present h - and hp -adaptive strategies suited for the discontinuous Galerkin formulation of the compressible laminar and Reynolds-averaged Navier–Stokes equations on unstructured grids, relying on a metric-based simplicial remeshing approach. An 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 both the metric field and the polynomial degree distribution map. The choice of refining either in h or p is driven by a smoothness indicator based on the decay of the modal coefficients in each element. The performance of the developed adaptation algorithms is assessed for the 2D laminar viscous flow past a NACA0012 airfoil, and for the 3D laminar viscous flows past a sphere and past a delta wing. The adaptive hp -strategy is applied to a 3D turbulent jet issued from a nozzle. Finally, the gain in accuracy provided by the adaptive algorithms with respect to uniformly refined simulations, for a given number of degrees of freedom, with polynomial degrees p = 1, 2, 3, is demonstrated. Highlights: h - and hp - adaptation methods based on a posteriori error estimation. Metric-based remeshing approach for unstructured discontinuous Galerkin methods. h - and hp - adaptive simulations of laminar compressible flows are performed. The method is extended to hybrid prismatic/tetrahedral meshes for RANS computations. Proved reduction of number of degrees of freedom compared to classical approaches.