Numerical solution of the Richards equation in unsaturated soil using the meshless Petrov–Galerkin method

Abstract

Nowadays, infiltration tactics are widely used to manage storm water in urban areas. These techniques are used and recognized around the world due to their benefits, such as reducing the negative consequences of urbanization, reducing storm water flow in sewage systems and recharging groundwater. Richards equation is one of the most well-known equations for simulating water infiltration in soil in the unsaturated area. In the present study, a one-dimensional approach to the numerical solution of Richards equation is presented using meshless Petrov–Galerkin method and Kirchhoff transformation. The results of this modeling have been compared with analytical solution, laboratory data, and finite difference and meshless numerical methods. Given that the proposed model can provide an accurate representation of water level changes in unsaturated soil compared to analytical solution, laboratory data, finite difference method and MQ-RBF with the root mean square error equal to 0.09, 1.02, 0.7 and 0.1, it can be claimed that the model can model the flow of water infiltration in unsaturated soil.