Method of asymptotic partial decomposition with discontinuous junctions - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Computers & Mathematics with Applications Année : 2022

Method of asymptotic partial decomposition with discontinuous junctions

Méthode de décomposition asymptotique partielle avec raccordements discontinus

Résumé

Method of asymptotic partial decomposition of a domain (MAPDD) proposed and justified earlier for thin domains (rod structures, tube structures consisting of a set of thin cylinders) generates some specific interface conditions between three-dimensional and one-dimensional parts. In the case of the heat equation these conditions ensure the continuity of the solution and continuity in average of the normal flux. However for some computational reasons the strong continuity condition for the solution may be undesirable. It may be preferable to replace it by more flexible condition of continuity in average over the interface cross section. In the present paper we introduce and justify this alternative junction condition allowing such discontinuity of the solution of both stationary and non-stationary problems. The closeness of solutions of these hybrid dimension problems to the solution of the fully three-dimensional setting is proved. At the discrete level, finite volume schemes are considered, an error estimate is established. The new version of the MAPDD is compared to the classical one via numerical tests. It shows better stability of the new scheme.
Fichier principal
Vignette du fichier
MAPDDNeum11.pdf (389.57 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Commentaire : Ce pdf est la version preprint de l'article (version soumise à l'éditeur, avant peer-reviewing)

Dates et versions

hal-03384810 , version 1 (19-10-2021)

Identifiants

Citer

Marie-Claude Viallon, Grigory Panasenko. Method of asymptotic partial decomposition with discontinuous junctions. Computers & Mathematics with Applications, 2022, 105, pp.75-93. ⟨10.1016/j.camwa.2021.11.017⟩. ⟨hal-03384810⟩
37 Consultations
49 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More