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

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

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
• Electronic ISSN: 1879-1778
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1446360