A Mathematical Framework for Particle Tracking Advection-Dispersion Across an Interface

A suitably scaled skew Brownian motion for a unique skewness parameter, or transmission coefficient, can be rigorously derived as the physical stochastic particle motion underlying advection and dispersion of solute concentrations in the presence of a discontinuous interface, leading to natural Monte-Carlo random walk simulations dating back to early routines proposed by G.J.M. Uffink (1985). In the case when the flow is parallel to the interface the algorithm is rigorously known to be a direct application of simulation by corresponding suitably scaled skew random walks. This talk will concern an approach to the case in which the flow direction is orthogonal to the interface.