Numerical solution of the Richards' equation in a two-dimensional bounded homogeneous soil
Abstract
In this work, we present a numerical solution to the linear Richards' equation in a two-dimensional bounded soil domain, modelling unsaturated flow through a homogeneous rectangular medium under various infiltration scenarios. The proposed method employs a two-step approach: time discretization is performed using a finite difference scheme, followed by spatial discretization using the method of fundamental solutions (MFS), a meshless technique known for its simplicity and accuracy. The resulting scheme is easy to implement and yields reliable estimates of soil moisture dynamics. The effectiveness and accuracy of the method are demonstrated through several test cases, including comparisons with available analytical solutions.
Fields of Study & Subjects
Soil and Unsaturated Flow
Groundwater flow and contamination studies
Numerical methods in engineering
Publication details
- Journal / source
- Journal of Hydraulic Research
- Volume
- 64
- Issue
- 1
- Pages
- 119–128
- Publication date
- 2 January 2026
- Language
- EN