Modeling of unsaturated flow through porous media using meshless methods

TL;DR

This paper introduces a meshless numerical method based on localized radial basis functions and Kirchhoff transformation to efficiently model unsaturated water flow in porous media, reducing computational time and improving accuracy.

Contribution

A novel meshless approach combining RBFs and Kirchhoff transformation for solving Richards equation in porous media.

Findings

Reduces computational time compared to traditional methods

Provides accurate solutions for 1D and 2D unsaturated flow

Successfully predicts water dynamics in soils

Abstract

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.