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.
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Journal articles
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
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Submitted on : Thursday, February 7, 2013 - 9:56:23 AM
Last modification on : Wednesday, July 29, 2015 - 1:23:50 AM

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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>

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