A finite-volume scheme for a kidney nephron model

Aurélie Edwards (1) , Nicolas Seguin (2) , Magali Tournus (2, 3)

1 Department of Chemical and Biological Engineering
2 LJLL - Laboratoire Jacques-Louis Lions
3 CRC (UMR_S 872) - Centre de Recherche des Cordeliers

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.

Domaines: Equations aux dérivées partielles [math.AP]

Aurélie Edwards, Nicolas Seguin, Magali Tournus. A finite-volume scheme for a kidney nephron model. ESAIM: Proceedings, 2012, 35, pp.287-292. ⟨10.1051/proc/201235029⟩. ⟨hal-00640061v2⟩