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Comment on “Diffusion theory for transport in porous media: Transition‐probability densities of diffusion processes corresponding to advection‐dispersion equations” by Eric M. LaBolle et al.

Because of its lack of numerical dispersion, the random-walk particle method (RWPM) presents an interesting alternative to solve the advection-dispersion equation. As shown by many authors [e.g., Ackerer and Kinzelbach, 1985; Kinzelbach, 1988; Tornpson and Gelhat, 1990; Uffink, 1990], the RWPM requires computation of a corrective term depending on the derivatives of the dispersion coefficients to preserve mass balance due to dispersion. This computation requires an adapted algorithm when the derivatives of the dispersion coefficients are not defined because of an abrupt change in velocity. This abrupt change is due either to the heterogeneity of the porous material or the discrete nature of the computed velocity field obtained by a numerical model. Labolle et al. [1998] address this very important issue and compare some algorithms used to preserve mass balance in a domain with constant coefficients in subdomains and discon-