Random walk in heterogeneous media: Comparison between sharp and smooth interface methods

Random walk methods are commonly used in the hydrological field to treat mass transport in heterogeneous medium. The heterogeneities can come from diffusion fields or from the capacities or porosities varying in space. Several techniques can be used in this case, (a) the introduction of a drift vector, based on the evolution of the diffusion coefficient along an artificial interface zone like in Spiller (2004), and (b), a special treatment for the particles arriving on an interface in the aim of Uffink (1985). We will present some simple test cases on 1 and 2 D situations in order to estimate the robustness and efficiency of these methods. Special focus will be made on the extension of RW in highly heterogeneous medium, when dealing with heat transport problem for example.