Finite analytic method for simulating water flow using water content-based Richards' equation

Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment. Richards' equation, which describes the movement of water flow in the vadose zone, is highly nonlinear and challenging to solve. Existing numerical methods often face issues such as numerical dispersion, oscillation, and mass non-conservation when spatial and temporal discretization conditions are not appropriately configured. To address these problems and achieve accurate and stable numerical solutions, a finite analytic method based on water content-based Richards' equation (FAM-W) is proposed. The performance of the FAM-W is compared with analytical solutions, Finite Difference Method (FDM), and Finite Analytic Method based on the pressure Head-based Richards' equation (FAM-H). Compared to analytical solution and other numerical methods (FDM and FAM-H), FAM-W demonstrates superior accuracy and efficiency in controlling mass balance errors, regardless of spatial step sizes. This study introduces a novel approach for modelling water flow in the vadose zone, offering significant benefits for water resources management.