张在勇, 王文科, 陆彦玮, 宫程程, 冉彬, 武泽宇. 改进型有限分析法模拟包气带土壤水分运移[J]. 农业工程学报, 2021, 37(18): 55-61. DOI: 10.11975/j.issn.1002-6819.2021.18.007
    引用本文: 张在勇, 王文科, 陆彦玮, 宫程程, 冉彬, 武泽宇. 改进型有限分析法模拟包气带土壤水分运移[J]. 农业工程学报, 2021, 37(18): 55-61. DOI: 10.11975/j.issn.1002-6819.2021.18.007
    Zhang Zaiyong, Wang Wenke, Lu Yanwei, Gong Chengcheng, Ran Bin, Wu Zeyu. Improved finite analytic method to simulate soil water movement in vadose zones[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2021, 37(18): 55-61. DOI: 10.11975/j.issn.1002-6819.2021.18.007
    Citation: Zhang Zaiyong, Wang Wenke, Lu Yanwei, Gong Chengcheng, Ran Bin, Wu Zeyu. Improved finite analytic method to simulate soil water movement in vadose zones[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2021, 37(18): 55-61. DOI: 10.11975/j.issn.1002-6819.2021.18.007

    改进型有限分析法模拟包气带土壤水分运移

    Improved finite analytic method to simulate soil water movement in vadose zones

    • 摘要: 近年来有限分析法被广泛应用于模拟土壤水分运移。混合型有限分析法通常使用一阶有限差分近似代替Richards方程中的时间导数项。尽管这种方法与其他的数值方法(例如有限差分法)相比,能获得精确度更高的数值解,但是当需要精细刻画陡峭湿润锋面向下传输过程时,需要对时间项的处理提出更高的要求。因此,该研究提出一种从时域和空间域获取局部解析解的改进型有限分析计算格式来克服上述问题。将改进的有限分析法的数值解、混合型有限分析的数值解、有限差分数值解与解析解定量化对比研究发现,改进型有限分析计算格式在较大空间步长条件下(空间步长为10 cm),能够获得精度较好的数值解,且能更好地控制质量平衡误差。此外,改进的有限分析法能获得与现有的软件(VSAFT2)相似的计算结果。该研究能为包气带水分运移模拟提供一种可靠的方法,推动区域土壤水资源的评价与管理。

       

      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.

       

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