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: |
adaptation modèle
Work (thermodynamics) Discretization General Physics and Astronomy discontinuous Galerkin method système hyperbolique 010103 numerical & computational mathematics estimation erreur Discretization error 01 natural sciences [SPI]Engineering Sciences [physics] adjoint problem relaxation Discontinuous Galerkin method Applied mathematics 0101 mathematics Mathematics [PHYS]Physics [physics] adjoint discretization adaptation Ecological Modeling Estimator méthode Galerkin discontinue General Chemistry Hyperbolic systems Computer Science Applications 010101 applied mathematics hyperbolic systems with relaxation sources Modeling and Simulation A priori and a posteriori model adaptation adaptation HP a posteriori estimates Relaxation (approximation) |
| 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 |
| 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 |
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