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

作者：Mohamed Kamel; Seaid Mohammed; Zahri Mostafa^*

来源：Journal of Computational and Applied Mathematics, 2013, 237(1): 614-632.

DOI：10.1016/j.cam.2012.07.014

• Conservation laws
• Stochastic differential equations
• Finite volume method
• Runge-Kutta scheme
• Traffic flow
• Buckley-Leverett equation

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.

• 出版日期2013-1-1