An improved method for the calculation of unsaturated–saturated water flow by coupling the FEM and FDM

Numerical modeling of water movement in both unsaturated soils and saturated groundwater aquifers is important for water resource management simulations. The development of efficient numerical algorithms for coupling unsaturated and saturated flow has been a long-lasting challenge in hydrologic modeling, especially for regional-scale modeling. In this study, a new method coupling the Finite Element Method (FEM) and Finite Difference Method (FDM), FE-FDM, is developed to solve Richards equation for simulating unsaturated–saturated water flow. The FEM is adopted to discretize the governing equation in the horizontal direction, while the FDM is used in the vertical direction. This method combines the advantages of FEM in domain discretization, especially for complex computational domain, and the advantages of FDM in modeling simplicity and efficiency. The validity of the new method is demonstrated with three test cases that show that the FE-FDM solutions are accurate and are applicable for regional scale problems. In the test cases, the FE-FDM solutions are compared with experimental data and numerical results calculated with common software packages including FEFLOW and COMSOL. This study verified that the FE-FDM is applicable for simulating water flow in the unsaturated–saturated zone.