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

Kamel Mohamed, Mohammed Seaid, Mostafa Zahri

• 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 twophase 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.