A Meshless Method with Radial Basis Function for Solving Unsaturated Flow in Heterogeneous Porous Media

Abstract

This paper presents a study for solving unsaturated flow in heterogeneous porous media using the meshless method with the radial basis function (RBF). For modeling the nonlinear hydrological process in unsaturated zone, an exponential model is introduced in the Richards equation such that we may obtain the linearized Richards equation. We adopt the multiquadric function as the RBF in the meshless method for solving the linearized Richards equation. For simulating the unsaturated flow problems in layered heterogeneous soils, the flux and the head must satisfy the continuity condition at the interface. Several examples are carried out for modeling the hydrological process in multielayered unsaturated soils. The results demonstrate that we only discretize by a set of points without tedious mesh generation and significantly enhance the applicability for solving unsaturated flow problems, especially in heterogeneous multielayered soils with extreme physical property contrasts.