Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions

The need of accurate and efficient numerical schemes to solve Richards’ equation is well recognized. This study is carried out to examine the numerical performances of the nonlinear multigrid method for numerical solving of the two-dimensional Richards’ equation modeling water flow in variably saturated porous media. The numerical approach is based on an implicit, second-order accurate time discretization combined with a vertex centered finite volume method for spatial discretization. The test problems simulate infiltration of water in 2D saturated–unsaturated soils with hydraulic properties described by van Genuchten–Mualem models. The numerical results obtained are compared with those provided by the modified Picard–preconditioned conjugated gradient (Krylov subspace) approach.