Random walk evaluation of Green’s functions for groundwater flow in heterogeneous aquifers

Abstract

The use of the Walk on Grid (WOG) approach for the reliable evaluation of the Green’s function associated with groundwater flow scenarios in heterogeneous geologic media is explored. The study rests on the observation that, while the Green’s function method (GFM) is one of the most significant and convenient approaches to tackle groundwater flow, Green’s function evaluation is fraught with remarkable difficulties in the presence of realistic groundwater settings taking place in complex heterogeneous geologic formations. Here WOG approach is used to simulate pressure dissipation by lattice random walk and establish a quantitative relationship between space-time distribution of random walkers and the Green’s function associated with the underlying flow problem. WOG-based Green’s function method is tested (a) in three scenarios where analytical formulations are available for the Green’s function and (b) in two groundwater flow systems with increased level of complexity. Our results show that WOG can (a) accurately evaluate the Green’s function, being highly efficient when the latter can be analytically expressed in terms of infinite series; and (b) accurately and efficiently evaluate temporal evolutions of hydraulic heads at target locations in the heterogeneous systems. As such, a WOG-based approach can be employed as an efficient surrogate model in scenarios involving groundwater flow in complex heterogeneous domains.