A NUMERICAL METHOD FOR TRANSPORT EQUATIONS WITH DISCONTINUOUS FLUX FUNCTIONS: APPLICATION TO MATHEMATICAL MODELING OF CELL DYNAMICS

被引：7
|
作者：
Aymard, Benjamin [1 ,2 ]
Clement, Frederique [2 ]
Coquel, Frederic [3 ,4 ]
Postel, Marie [1 ,5 ]
机构：
[1] Univ Paris 06, Lab Jacques Louis Lions, UMR 7598, F-75005 Paris, France
[2] Ctr Rech Inria Paris Rocquencourt, F-78153 Le Chesnay, France
[3] Ecole Polytech, CNRS, F-91128 Palaiseau, France
[4] Ecole Polytech, CMAP, UMR 7641, F-91128 Palaiseau, France
[5] CNRS, UMR 7598, F-75005 Paris, France
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2013年 / 35卷 / 06期
关键词：
kinetic equations; finite volumes; discontinuous coefficients; cell dynamics; CONSERVATION-LAWS; APPROXIMATION;
D O I：
10.1137/120904238
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 one-and two-dimensional 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.
引用
收藏
页码：A2442 / A2468
页数：27
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