×

A finite volume method for scalar conservation laws with stochastic time-space dependent flux functions. (English) Zbl 1252.65152

Summary: 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 [V. Rosanov, “Calculation oft interaction of non-steady shock waves with obstacles”, J. Comput. Math. Phys. USSR 1, 267–279 (1961)] 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.

MSC:

65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
PDFBibTeX XMLCite
Full Text: DOI