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

Francesca Basile (1, 2, 3) , Jean-Baptiste Chapelier (3) , Marta de La Llave Plata (4) , Romain Laraufie (2) , Pascal Frey (5)

1 SU - Sorbonne Université
2 Airbus Operation S.A.S.
3 DAAA, ONERA, Université Paris-Saclay [Châtillon]
4 DMPE, ONERA, Université de Toulouse [Toulouse]
5 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

In this paper, we present hand hp-adaptative 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 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.

Domaines: Mécanique des fluides [physics.class-ph]

Francesca Basile, Jean-Baptiste Chapelier, Marta de La Llave Plata, Romain Laraufie, Pascal Frey. Unstructured h- and hp- adaptive strategies for discontinuous Galerkin methods based on a posteriori error estimation for compressible flows. 2021. ⟨hal-03380622⟩