Simulating diffusions with piecewise constant coefficients using a kinetic approximation

Using a kinetic approximation of a linear diffusion operator, we propose an algorithm that allows one to deal with the simulation of a multi-dimensional stochastic process in a media which is locally isotropic except on some surface where the diffusion coefficient presents some discontinuities. Basic numerical examples are given in dimensions one to three on PDEs or stochastic PDEs with or without source terms. Finally, we compute the hydro-dynamic load in a porous media in the nuclear waste context.