PARTICLE-TRACKING EQUATIONS FOR THE SOLUTION OF THE ADVECTION-DISPERSION EQUATION WITH VARIABLE-COEFFICIENTS

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 coefficient s. The derivation is based on integration by parts of the advection-di spersion 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 v elocity to account for variability in the dispersion coefficients and thus provide physically reasonable results.