Equivalence conditions between linear Lagrangian finite element and node-centred finite volume schemes for conservation laws in cylindrical coordinates

Abstract : A complete set of equivalence conditions, relating the mass-lumped Bubnov-Galerkin finite element (FE) scheme for Lagrangian linear elements to node-centred finite volume (FV) schemes, is derived for the first time for conservation laws in a three-dimensional cylindrical reference. Equivalence conditions are used to devise a class of FV schemes, in which all grid-dependent quantities are defined in terms of FE integrals. Moreover, all relevant differential operators in the FV framework are consistent with their FE counterparts, thus opening the way to the development of consistent hybrid FV/FE schemes for conservation laws in a three-dimensional cylindrical coordinate system. The two-dimensional schemes for the polar and the axisymmetrical cases are also explicitly derived. Numerical experiments for compressible unsteady flows, including expanding and converging shock problems and the interaction of a converging shock waves with obstacles, are carried out using the new approach. The results agree fairly well with one-dimensional simulations and simplified models.
Type de document :
Article dans une revue
International Journal for Numerical Methods in Fluids, Wiley, 2014, 74 (7), pp.514-542. 〈http://onlinelibrary.wiley.com/doi/10.1002/fld.3862/abstract〉. 〈10.1002/fld.3862〉
Liste complète des métadonnées

Littérature citée [42 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00935561
Contributeur : Dante De Santis <>
Soumis le : jeudi 23 janvier 2014 - 16:23:19
Dernière modification le : jeudi 11 janvier 2018 - 06:22:35
Document(s) archivé(s) le : jeudi 24 avril 2014 - 05:15:12

Fichier

output.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Dante De Santis, Gianluca Geraci, Alberto Guardone. Equivalence conditions between linear Lagrangian finite element and node-centred finite volume schemes for conservation laws in cylindrical coordinates. International Journal for Numerical Methods in Fluids, Wiley, 2014, 74 (7), pp.514-542. 〈http://onlinelibrary.wiley.com/doi/10.1002/fld.3862/abstract〉. 〈10.1002/fld.3862〉. 〈hal-00935561〉

Partager

Métriques

Consultations de la notice

299

Téléchargements de fichiers

164