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

页码：A2442 / A2468

页数：27

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