Unstructured h- and hp-adaptive strategies for discontinuous Galerkin methods based on a posteriori error estimation for compressible flows

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.