Improved Linear and Nonlinear Iterative Methods for Rainfall Infiltration Simulation

Abstract

AbstractThe linear infiltration equations obtained by discretizing Richards’ equation need to be solved iteratively, including two approaches of linear and nonlinear iterations. The first method is to use numerical methods to directly numerically discretize Richards’ equations to obtain nonlinear ordinary differential equations and then use nonlinear iterative methods to iteratively solve, such as Newton’s method (Radu et al. in On the convergence of the Newton method for the mixed finite element discretization of a class of degenerate parabolic equation. Numerical mathematics and advanced applications. Springer, pp 1194–1200, 2006), Picard method (Lehmann and Ackerer 1998), and the L-method (List and Radu 2016). The Picard method can be considered as a simplified Newton method, which linearly converges.