Unsaturated Transport Modeling: Random‐Walk Particle‐Tracking as a Numerical‐Dispersion Free and Efficient Alternative to Eulerian Methods

Abstract Lagrangian methods, such as the random‐walk particle‐tracking (RWPT), are often qualified a potentially valuable alternative to error‐prone Eulerian methods for simulating solute transport in unsaturated porous media. Yet, RWPT method has not yet been validated against ‐ and compared currently used solutions under range of typical conditions. This paper presents new implementation approach advective dispersive problems variably saturated We first show that, previously demonstrated heterogeneous dispersion tensor, using an interpolation scheme algorithm performs well with abrupt changes water content. The model is then simple 1D uniform problem, which analytical solution exist, variety 3D numerical different schemes implemented Hydrus software suite. Results while significantly suffer from case coarse spatial discretization simulation domain, provides accurate all problems. Furthermore, reproduces accurately flow conditions (infiltration, evaporation). Moreover, appears be orders magnitude faster than its solve problem. Thus, should seen attractive, stable efficient vadose zone, especially complex large