Finite element algorithm for solving one-dimensional Richards’ equation

Abstract

Accurate, efficient, robust, and stable numerical solution of Richards’ equation for variably saturated-unsaturated water flow through porous media is an extremely challenging task for any numerical integrator due to its highly nonlinear behavior. In this study, we have solved a one-dimensional Richards’ equation that frequently describes saturated-unsaturated water flow in homogeneous soil layers. The obtained solution is a set of an ordinary differential equation derived from mass conservation principles. We have used the finite element method for domain discretization of the governing equation, while backward Euler finite difference technique is employed for temporal discretizing to simulate infiltration and sharp fronts. As a result, mass balance errors have been reduced. The validity of the method is demonstrated with three test cases that show that the presented solution technique is explicitly integrable, has no numerical complexity. It is accurate, computationally efficient, and robust, as well as, can extend to simulate heterogeneous soils.