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v1 (13-11-2012)

v2 (07-02-2013)

A NUMERICAL METHOD FOR KINETIC EQUATIONS WITH DISCONTINUOUS EQUATIONS : APPLICATION TO MATHEMATICAL MODELING OF CELL DYNAMICS

Benjamin Aymard 1, Frédérique Clément 2, Frédéric Coquel 1, 3, Marie Postel 1

(07/02/2013)

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.

1 :	Laboratoire Jacques-Louis Lions (LJLL)
	CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI
2 :	SISYPHE (SIgnals and SYstems in PHysiology and Engineering) (INRIA Rocquencourt)
	INRIA
3 :	CNRS and CMAP (UMR 7641)
	CNRS : UMR7641

Équipe de recherche : LJLL

Domaine

:

Informatique/Analyse numérique

Mots Clés : Kinetic equations – Finite volumes – Discontinuous coefficients – Cell dynamics

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Contributeur : Christian David <>

Soumis le : Jeudi 7 Février 2013, 09:56:23

Dernière modification le : Jeudi 7 Février 2013, 09:58:46