  In this study, we focus on the modelling of infiltration process in porous
media. We use the meshless techniques for efficiently solving the Richards
equation which describes unsaturated water flow through soils. The design of
approximate numerical methods for the Richards equation remains computationally
challenging and requires the development of efficient numerical techniques.
This difficulty is mainly due to the nonlinearity of the unsaturated hydraulic
conductivity and the capillary pressure function. In this study, we develop a
new method based on the localized radial basis function (RBF) and the Kirchhoff
transformation technique in order to solve Richards equation in one and
two-dimensional homogeneous medium. Our approach using the multiquadric radial
basis function allows us to reduce the computational time and provide accurate
numerical solutions. The proposed method does not require mesh generation.
Picard's iterations are used to linearize the resulting nonlinear problem
obtained using the Kirchhoff transformation technique. The numerical
simulations show the capability of the proposed numerical techniques in
predicting the dynamics of water through unsaturated soils.

Numerical Analysis;Numerical Analysis;Fluid Dynamics