Localized RBF methods for modeling infiltration using the Kirchhoff-transformed Richards equation

We develop a new approach to solve the nonlinear Richards equation based on Kirchhoff transformation and localized radial basis function (LRBF) techniques. Our aim is reduce nonlinearity of governing apply LRBF methods for modeling unsaturated flow through heterogeneous soils. In our methodology, we propose special techniques which deal with heterogeneity medium in order where used Brooks Corey model capillary pressure power-law relation saturation relative permeability function. The allows us avoid technical issues encountered due soil equation. resulting Kirchhoff-transformed solved using have advantages terms computational cost since they do not require mesh generation. Furthermore, lead system sparse matrix ill-conditioned issues. To validate developed predicting dynamics porous media, numerical experiments are performed one, two, three-dimensional results demonstrate efficiency accuracy proposed infiltration