Geodesic
A finite-volume scheme for a kidney nephron model
Aurélie Edwards1 ; Nicolas Seguin2 ; Magali Tournus2
1 UPMC Univ Paris 06, Univ Paris 05, INSERM UMRS872, and CNRS ERL7226, Laboratoire de génomique, physiologie et physiopathologie rénales, Centre de Recherche des Cordeliers, F-75006, Paris, France
2 UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France
ESAIM. Proceedings, Tome 35 (2012), pp. 287-292.

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We present a finite volume type scheme to solve a transport nephron model. The model consists in a system of transport equations with specific boundary conditions. The transport velocity is driven by another equation that can undergo sign changes during the transient regime. This is the main difficulty for the numerical resolution. The scheme we propose is based on an explicit resolution and is stable under a CFL condition which does not depend on the stiffness of source terms.
DOI : 10.1051/proc/201235029

Aurélie Edwards 1 ; Nicolas Seguin 2 ; Magali Tournus 2

1 UPMC Univ Paris 06, Univ Paris 05, INSERM UMRS872, and CNRS ERL7226, Laboratoire de génomique, physiologie et physiopathologie rénales, Centre de Recherche des Cordeliers, F-75006, Paris, France
2 UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France 
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Aurélie Edwards; Nicolas Seguin; Magali Tournus. A finite-volume scheme for a kidney nephron model. ESAIM. Proceedings, Tome 35 (2012), pp. 287-292. doi : 10.1051/proc/201235029. http://geodesic.mathdoc.fr/articles/10.1051/proc/201235029/

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