A new robust and efficient iterative scheme for a degenerated non-linear parabolic problem

Abstract

The flow of water through the soil is modeled mathematically by the Richards equation. This doubly degenerate nonlinear equation is difficult to solve, even more nonlinearity and degeneration make the design of numerical schemes for this problem a challenging task. According to the literature, the implicit methods are the ones that give the best results since the schemes obtained allow to simulate the degenerate problem, however these produce nonlinear problems that must be solved by means of linearization methods. In this investigation a new numerical scheme of linearization of the Richards equation is developed. A totally implicit Euler scheme is used to discretize time and finite elements to discretize space, however, these schemes should work for any spatial discretization chosen. A more robust and faster scheme was achieved (in terms of number of iterations and total machine time used) than those already existing.