A hybrid finite volume method for advection equations and its applications in population dynamics

Léon Matar Tine 1, 2 Chang Yang 3
1 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We present in this paper a very adapted finite volume numerical scheme for transport type-equation. The scheme is an hybrid one combining an anti-dissipative method with down-winding approach for the fux [8, 6] and an high accurate method as the WENO5 one [13]. The main goal is to construct a scheme able to capture in exact way the numerical solution of transport type-equation without artifact like numerical diffusion or without "stairs" like oscillations and this for any regular or discontinuous initial distribution. This kind of numerical hybrid scheme is very suitable when properties on the long term asymptotic behavior of the solution are of central importance in the modeling what is often the case in context of population dynamics where the final distribution of the considered population and its mass preservation relation are required for prediction.
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Numerical Methods for Partial Differential Equations, Wiley, 2016, 〈10.1002/num.22134〉
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https://hal.inria.fr/hal-01421825
Contributeur : Leon Matar Tine <>
Soumis le : jeudi 22 décembre 2016 - 22:46:36
Dernière modification le : mercredi 11 avril 2018 - 01:55:38

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Léon Matar Tine, Chang Yang. A hybrid finite volume method for advection equations and its applications in population dynamics. Numerical Methods for Partial Differential Equations, Wiley, 2016, 〈10.1002/num.22134〉. 〈hal-01421825〉

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