A numerical solver for large scale three-dimensional variable saturated groundwater flow

Abstract

Mathematical models play a vital role in hydrological forecasting and water management, particularly regarding the understanding of the long-term behaviour of groundwater flow. One of the most commonly studied models of groundwater flow is Richards equation, which describes the movement of water in both unsaturated and saturated soils. Despite its importance, this equation is generally avoided in continental-scale modelling due to its recognised computational difficulty. Here we present a novel, open-source numerical package for solving Richards equation in three dimensions that is suitable for studying groundwater flow at a variety of spatial scales. Our solver utilises Firedrake, a flexible software package for solving partial differential equations via the Discontinuous Galerkin finite element method. We demonstrate how our solver can easily handle small scale problems (order of metres) efficiently and accurately. We then present a large-scale case study of groundwater flow in the Lower Murrumbidgee basin, located in New South Wales, Australia, which has an area of around 3600 km squared. Our simulation incorporates data made available by the Bureau of Meteorology (BoM) to model the stratigraphy of the basin, which consists of three layers of varying depth, as well as estimates of annual rainfall and current depth to water table. We show that our solver can accurately simulate flow dynamics over decades at a spatial scale well beyond previous studies. Show more