Time domain random walks for hydrodynamic transport in heterogeneous media

Anna Russian (1) , Marco Dentz (2) , Philippe Gouze (1)

1 Géosciences Montpellier
2 IDAEA - Institute of Environmental Assessment and Water Research

We derive a general formulation of the time domain random walk (TDRW) approach to model the hydrodynamic transport of inert solutes in complex geometries and heterogeneous media. We demonstrate its formal equivalence with the discretized advection-dispersion equation and show that the TDRW is equivalent to a continuous time random walk (CTRW) characterized by space-dependent transition times and transition probabilities. The transition times are exponentially distributed. We discuss the implementation of different concentration boundary conditions and initial conditions as well as the occurrence of numerical dispersion. Furthermore, we propose an extension of the TDRW scheme to account for mobile-immobile multirate mass transfer. Finally, the proposed TDRW scheme is validated by comparison to analytical solutions for spatially homogeneous and heterogeneous transport scenarios.

Mots clés: time domain random walk; continuous time random walk; transport; multirate mass transfer

Domaines: Géophysique [physics.geo-ph]

Anna Russian, Marco Dentz, Philippe Gouze. Time domain random walks for hydrodynamic transport in heterogeneous media. Water Resources Research, 2016, 52 (5), pp.3309-3323. ⟨10.1002/2015WR018511⟩. ⟨hal-01356319⟩