The equations of motion of a particle are derived for the random walk (or discrete parcel particle tracking) method used for the solution of the advection-dispersion equation with spatially variable coefficients. The derivation is based on integration by parts of the advection-dispersion equation, rather than on stochastic-integral calculus used in other derivations. The analysis highlights the fundamental nature of the drift term, which is the term that needs to be added to the mean velocity to account for variability in the dispersion coefficients and thus provide physically reasonable results.
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