Application of modified iterative method to simulate rainfall infiltration in unsaturated soils

Abstract

A modified Gauss-Seidel iterative method (MP(m)-GS) with multistep preconditioner is developed to solve partial differential equations of rainfall infiltration. The finite difference method (FDM) is applied to numerical discretization. Furthermore, a system of linear equations is solved using an iterative scheme. For some unfavorable numerical conditions, such as large initial conditions, classical Picard iterative method usually has low accuracy and computational efficiency. Conventional linear iterative methods have a slower convergence rate, such as Gauss-Seidel (GS) and Jacobi iterative methods, particularly for small discrete space step size. Thus, MP(m)-GS is developed to simulate rainfall infiltration into unsaturated soils. The analytical solutions are employed to verify the proposed methods. The results indicate that the MP(m)-GS has higher computational efficiency and accuracy than the improved Picard methods. Compared with the conventional linear iterative methods GS and SOR, MP(m)-GS also demonstrates faster convergence rate and higher computation efficiency. The results show nice applications in modeling rainfall infiltration in unsaturated soils.