A new numerical treatment of soil heterogeneity for modeling unsaturated flow

We develop a new approach to solve the Richardson-Richards equation for modeling unsaturated flow through heterogeneous porous media. The main idea of the proposed techniques is the use of the Kirchhoff transformation, the Brooks and Corey model for the capillary pressure function and a power-law relation in saturation for the relative permeability function. The new approach allows us to avoid the technical issues encountered in the Kirchhoff transformation due to soil heterogeneity. This transformation is applied to reduce the nonlinearity of the model which is solved using a numerical scheme based on a local radial basis function method (RBF). To validate the developed approach for predicting the dynamics of unsaturated flow in porous media, numerical experiments are performed in one, two, and three-dimensional soils. The numerical results demonstrate the efficiency and accuracy of the proposed techniques for modeling infiltration through heterogeneous soils.