Méthode d'adaptation de discrétisation et de modèle basée sur l'adjoint pour les systèmes hyperboliques avec relaxation

Autor: Dylan Dronnier, Florent Renac
Přispěvatelé: Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), DAAA, ONERA, Université Paris-Saclay (COmUE) [Châtillon], ONERA-Université Paris Saclay (COmUE)
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2019, 17 (2), pp.750-772. ⟨10.1137/18M120676X⟩
ISSN: 1540-3459
1540-3467
DOI: 10.1137/18M120676X⟩
Popis: International audience; In this work, we use an adjoint-weighted residuals method for the derivation of an a posteriori model and discretization error estimators in the approximation of solutions to hyperbolic systems with stiff relaxation source terms and multiscale relaxation rates. These systems are parts of a hierarchy of models where the solution reaches different equilibrium states associated to different relaxation mechanisms. The discretization is based on a discontinuous Galerkin method which allows to account for the local regularity of the solution during the discretization adaptation. The error estimators are then used to design an adaptive model and discretization procedure which selects locally the model, the mesh, and the order of the approximation and balances both error components. Coupling conditions at interfaces between different models are imposed through local Riemann problems to ensure the transfer of information. The reliability of the present hpm-adaptation procedure is assessed on different test cases involving a Jin--Xin relaxation system with multiscale relaxation rates, and results are compared with standard hp-adaptation.
Databáze: OpenAIRE
Popis
Abstrakt:International audience; In this work, we use an adjoint-weighted residuals method for the derivation of an a posteriori model and discretization error estimators in the approximation of solutions to hyperbolic systems with stiff relaxation source terms and multiscale relaxation rates. These systems are parts of a hierarchy of models where the solution reaches different equilibrium states associated to different relaxation mechanisms. The discretization is based on a discontinuous Galerkin method which allows to account for the local regularity of the solution during the discretization adaptation. The error estimators are then used to design an adaptive model and discretization procedure which selects locally the model, the mesh, and the order of the approximation and balances both error components. Coupling conditions at interfaces between different models are imposed through local Riemann problems to ensure the transfer of information. The reliability of the present hpm-adaptation procedure is assessed on different test cases involving a Jin--Xin relaxation system with multiscale relaxation rates, and results are compared with standard hp-adaptation.
ISSN:15403459
15403467
DOI:10.1137/18M120676X⟩