Abstract:
Abstract: Finite Analytic Method (FAM) has widely been used to solve the Richards equation in recent years. The first-order finite difference approximation can usually be utilized in the hybrid FAM (HFAM) to handle the time derivative term during solution. To some extent, the HFAM can obtain satisfactory results, compared with other numerical methods, such as the modified picard Finite Difference (MPFD) method. However, large errors can also be found using the HFAM to simulate the characteristics of sharp wetting fronts during the infiltration process in the vadose zone. Therefore, a better method is required to handle the time derivative term. In this study, an improved FAM (IFAM) was proposed to accurately simulate the soil water movement in the vadose zone. The IFAM was selected to obtain local analytic solutions from both the time and space domain simultaneously, due mainly to totally different from the HFAM method. Three cases were also considered to systematically evaluate the performance of IFAM. In all cases, the one-dimensional vertical soil columns were set as 100 cm. In the first case, the upper boundary condition was a constant flux boundary, and the lower boundary was a constant pressure head. Three soil columns were discretized into 100, 50, and 10 elements, respectively. The Finite Difference Method (FDM), HFAM, analytic solution, and IFAM were utilized to solve the Richards equation for better comparison. In the second case, both upper and lower boundary conditions were constant pressure heads. The vertical discretization spacing was set as 1 cm. The water movement was then simulated in the vadose zone using IFAM and VSAFT2 (a commonly-used software based on the Finite Element Method (FEM) to solve the Richards equation). In the third case, the upper boundary condition was also assumed to be a flux boundary, and the flux was equal to the amount of evaporation and rainfall. The lower boundary condition was a constant pressure head. The results of the first case showed that the best numerical results was achieved in the IFAM among all numerical methods. Furthermore, the minimum mass balance error was obtained in IFAM even under the condition of larger spatial steps (spatial step equal to 10 cm), compared to the analytical solution. The results from both the second and third cases showed that there was similar solutions to the IFAM in contrast with VSAFT 2. Consequently, the IFAM can widely be expected to significantly improve the numerical accuracy of the solution to the Richards equation under the larger vertical discretization spacing. This finding can also provide a better way for the simulation of water movement in the vadose zone, particularly for sustainable water resources management and ecological protection.