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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:237

Article

Mohamed, Kamel²  Seaid, Mohammed³  Zahri, Mostafa¹ 

[1] Univ Taibah, Fac Sci, Dept Math, Medina, Saudi Arabia

[2] Univ Taibah Madinah, Fac Sci Appl, Dept Comp Sci, Medina, Saudi Arabia

[3] Univ Durham, Sch Engn & Comp Sci, Durham DH1 3LE, England

关键词: Conservation laws;    Stochastic differential equations;    Finite volume method;    Runge-Kutta scheme;    Traffic flow;    Buckley-Leverett equation;   

DOI  :  10.1016/j.cam.2012.07.014

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free