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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 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.
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https://hal.archives-ouvertes.fr/hal-03380622
Contributor : Francesca Basile Connect in order to contact the contributor
Submitted on : Friday, October 15, 2021 - 4:39:23 PM
Last modification on : Wednesday, November 24, 2021 - 4:43:00 PM

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  • HAL Id : hal-03380622, version 1

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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⟩

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