An improved method for the calculation of unsaturated\u2013saturated water flow by coupling the FEM and FDM

Yulong Gao,Chunmiao Zheng,Shuping Yi,Shengyan Pu

doi:10.1038/s41598-019-51405-4

Abstract

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.

Highlights

Understanding the hydrologic cycle is critical for proper management of groundwater resources
The DHI21,22 developed a more comprehensive saturated-unsaturated flow model, based on the Finite Difference Method (FDM), MIKE SHE (Système Hydrologique Européen), where the unsaturated flow is simplified to 1-D in Richards equation while saturated flow is controlled by 3-D Boussinesq equation
This study developed a new numerical method, FE-FDM by coupling Finite Element Method (FEM) and FDM, to solve the Richards equation for simulating unsaturated–saturated water flow

Summary

Ks Ks

Where Ks is the saturated hydraulic conductivity, Se is degree of saturation which could be expressed by: Se = θ − θr θs − θr (5). The specific moisture capacity can be given by:. The objective of this section is to obtain the numerical form of Richards equation by FE-FDM. The FEM is used to discretize the governing equation in in horizontal direction while the FDM is used in the vertical direction. Finite element method in the horizontal direction. The governing equation for horizontal flow is discretized by the FEM. According to the Galerkin method, the discrete form in horizontal direction is constructed as follows:

NiNjdxdy dHik dt

Verification Examples

Conclusion

Findings

Additional information