Interface formulation for generalized finite difference method for solving groundwater flow

Abstract

Simulation of realistic groundwater flow phenomena in unsaturated porous layered media needs to consider all the environmental features that influence the governing equation of the dynamics of the process, namely, the Richards equation. In the stationary case, the latter is a nonlinear parabolic expression whose numerical solution requires an adequate discretization of the differential operator for approximating its solution accurately to avoid numerical inaccuracies that yield unrealistic numerical oscillations between soil layers. A reliable spatial discretization can be obtained via a generalized finite differences scheme used as a meshless method, which allows the pose of discrete expressions for differential operators, including the discontinuous coefficients that describe the changes in permeability in different media. The key idea is to use a frontier nodal balance expression written so that the amount of water is conserved at the interface nodes. The proposed discretization’s robustness and accuracy are demonstrated by presenting several benchmark problems.