Reply to comment by D.‐H. Lim on “Diffusion processes in composite porous media and their numerical integration by random walks: Generalized stochastic differential equations with discontinuous coefficients”

Abstract

[1] We thank Lim [2005] for providing this opportunity to clarify the restrictions and confirm the applicability of the results of LaBolle et al. [2000]. LaBolle et al. [2000] develop generalized stochastic differential equations (SDE) that converge to advection dispersion equations with discontinuous dispersion tensor D. The problem of interest here relates to equation (15a) of LaBolle et al. [2000] and its application in the numerical simulation of random walks converging to advection dispersion equations with discontinuous coefficients. In one dimension this equation can be written as