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A finite volume method for scalar conservation laws with stochastic time-space dependent flux function

Mohamed, K.; Seaid, M.; Zahri, M.

A finite volume method for scalar conservation laws with stochastic time-space dependent flux function Thumbnail


Authors

K. Mohamed

M. Zahri



Abstract

We propose a new finite volume method for scalar conservation laws with stochastic time–space dependent flux functions. The stochastic effects appear in the flux function and can be interpreted as a random manner to localize the discontinuity in the time–space dependent flux function. The location of the interface between the fluxes can be obtained by solving a system of stochastic differential equations for the velocity fluctuation and displacement variable. In this paper we develop a modified Rusanov method for the reconstruction of numerical fluxes in the finite volume discretization. To solve the system of stochastic differential equations for the interface we apply a second-order Runge–Kutta scheme. Numerical results are presented for stochastic problems in traffic flow and two-phase flow applications. It is found that the proposed finite volume method offers a robust and accurate approach for solving scalar conservation laws with stochastic time–space dependent flux functions.

Citation

Mohamed, K., Seaid, M., & Zahri, M. (2013). A finite volume method for scalar conservation laws with stochastic time-space dependent flux function. Journal of Computational and Applied Mathematics, 237(1), 614-632. https://doi.org/10.1016/j.cam.2012.07.014

Journal Article Type Article
Publication Date Jan 1, 2013
Deposit Date Dec 3, 2013
Publicly Available Date Nov 30, 2015
Journal Journal of Computational and Applied Mathematics
Print ISSN 0377-0427
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 237
Issue 1
Pages 614-632
DOI https://doi.org/10.1016/j.cam.2012.07.014
Keywords Conservation laws, Stochastic differential equations, Finite volume method, Runge–Kutta scheme, Traffic flow, Buckley–Leverett equation.

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