Abstract The random walk particle tracking method has become an important tool for the uncertainty assessment of solute transport models due to its computational efficiency and the non-existence of numerical dispersion. Yet, in highly heterogeneous aquifers the smoothness assumption of the velocity field, requisite for a correct solution of the random walk equations, may not hold anymore. Three different numerical methods to overcome this problem are numerically evaluated. The results demonstrate that in an aquifer with an isotropic spatial correlation, and following a multi-Gaussian random function with a small connectivity of extreme values, all techniques are able to model solute transport correctly, even for a hydraulic conductivity variance of s ²_lnK = 4.

Keywords heterogeneity; local mass conservation; numerical implementation; random walk particle tracking; solute transport