A numerical method for kinetic equations with discontinuous equations : application to mathematical modeling of cell dynamics

Abstract : Abstract: In this work, we propose a numerical method to handle discontinuous fluxes arising in transport-like equations. More precisely, we study hyperbolic PDEs with flux transmission conditions at interfaces between subdomains where coefficients are discontinuous. A dedicated finite volume scheme with a limited high order enhancement is adapted to treat the discontinuities arising at interfaces. The validation of the method is done on 1D and 2D toy problems for which exact solutions are available, allowing us to do a thorough convergence study. We then apply the method to a biological model focusing on complex cell dynamics, that initially motivated this study, and illustrates the full potentialities of the scheme.
Type de document :
Article dans une revue
SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2013, 35 (6), 27 p. <10.1137/120904238>


https://hal.archives-ouvertes.fr/hal-00751454
Contributeur : Christian David <>
Soumis le : jeudi 7 février 2013 - 09:56:23
Dernière modification le : mercredi 12 octobre 2016 - 01:23:57

Fichier

R12083.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

INRIA | UPMC | LJLL | CMAP | USPC

Citation

Benjamin Aymard, Frédérique Clément, Frédéric Coquel, Marie Postel. A numerical method for kinetic equations with discontinuous equations : application to mathematical modeling of cell dynamics. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2013, 35 (6), 27 p. <10.1137/120904238>. <hal-00751454v2>

Exporter

Partager

Métriques

Consultations de
la notice

334

Téléchargements du document

118