A Numerical Method for Transport Equations with Discontinuous Flux Functions: Application to Mathematical Modeling of Cell Dynamics | Zendy

Benjamin Aymard | Zendy; Frédérique Clément | Zendy; Fré́dé́ric Coquel | Zendy; Marie Postel | Zendy

Open Access

A Numerical Method for Transport Equations with Discontinuous Flux Functions: Application to Mathematical Modeling of Cell Dynamics

Author(s) -

Benjamin Aymard,

Frédérique Clément,

Fré́dé́ric Coquel,

Marie Postel

Publication year - 2013

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/120904238

Subject(s) - classification of discontinuities , convergence (economics) , finite volume method , mathematics , numerical analysis , scheme (mathematics) , mathematical analysis , mathematical optimization , mechanics , physics , economics , economic growth

International audienceAbstract: 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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