Innovative modelling of 3D unsaturated flow in porous media by coupling independent models for vertical and lateral flows

Abstract

Unsaturated groundwater flows are mathematically represented by the Richards equation. Hitherto, in Hydrology, solutions of this equation mainly serve as an alimentation of the source term for the surface runoff modelling. Therefore, the complete resolution of the 3D model looks surplus to requirements and the infiltration is dealt either thanks to 1D vertical modelling of the Richards equation or through derivate models (like e.g. the Green–Ampt infiltration model or the Horton law), thus ignoring eventual horizontal transfers.Nowadays, the request for more detailed information is real, and the physics of groundwater unsaturated flow needs to be represented more reliably. This information could be furnished by the resolution of the complete 3D model, but, although numerically mastered and well documented, it is very costly for large scale–both in time and space–real applications (climate change adaptation of watersheds).The authors propose an original solution decoupling the 3D equations into 1D vertical equations and a 2D depth-integrated horizontal equation. The aim is to consider independent vertical columns of infiltration coupled with lateral transfer of mass through the boundary conditions. On this basis, they postulate that the mass transfers in the three dimensions are correctly represented. This way problematic like the supply of the aquifers, the re-emergence of groundwater to surface water or especially the capability of memorization of past rainy events …could be reliably depicted.The two coupled models are solved on a unique numerical frame. A cell-centred Finite Volume method is used to solve the parabolic partial differential equations. The spatial derivatives are approximate by a second order central difference scheme, while the time splitting follows an implicit backward Euler scheme coupled with Picard iteration.The method has been tested and its reliability assessed on different theoretical two-dimensional cross-sectional test cases representing infiltration phenomena.