A Partitioned Finite Element Method for power-preserving discretization of open systems of conservation laws - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue IMA Journal of Mathematical Control and Information Année : 2020

A Partitioned Finite Element Method for power-preserving discretization of open systems of conservation laws

Résumé

This paper presents a structure-preserving spatial discretization method for distributed parameter port- Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and geometries. For these systems, a partitioned finite element method (PFEM) is derived, based on the integration by parts of one of the two conservation laws written in weak form. The non-linear one-dimensional shallow-water equation (SWE) is first considered as a motivation example. Then, the method is investigated on the example of the non-linear two-dimensional SWE. Complete derivation of the reduced finite-dimensional port-Hamiltonian system (pHs) is provided and numerical experiments are performed. Extensions to curvilinear (polar) coordinate systems, space-varying coefficients and higher-order pHs (Euler–Bernoulli beam equation) are provided.
Fichier principal
Vignette du fichier
Ruiz_27418.pdf (1.72 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03149105 , version 1 (22-02-2021)

Identifiants

Citer

Flávio Luiz Cardoso-Ribeiro, Denis Matignon, Laurent Lefèvre. A Partitioned Finite Element Method for power-preserving discretization of open systems of conservation laws. IMA Journal of Mathematical Control and Information, 2020, pp.0. ⟨10.1093/imamci/dnaa038⟩. ⟨hal-03149105⟩

Collections

UGA LCIS ANR
21 Consultations
44 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More