Abstract Simulation of variably saturated soil water flow requires the use of pressure head, or soil moisture, or a switching between the two, as the primary variable for solving Richards’ equation. Under unfavorable conditions, such as heterogeneity, rapidly changing atmospheric boundary, or sudden infiltration into dry soils, the traditional non-switching method suffers from numerical difficulties. Solving this problem with a primary variable switching method is less preferred due to the mathematical complexity. While the Picard method is more popular for solving the non-switching models due to its simplicity and stability, two different forms of Richards’ equation are combined into one numerical scheme for switching under specific hydraulic conditions. The method is successfully implemented in a one-dimensional model solved by a Picard iteration scheme. A threshold saturation based on the soil moisture retention relation is used for switching between either form of the Richards’ equation. The method developed here is applicable for simulating variably saturated subsurface flow in heterogeneous soils. Compared with traditional methods, the proposed model conserves mass well and is numerically more stable and efficient.

中文翻译：

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切换理查兹方程以模拟不利条件下的土壤水分运动

摘要 可变饱和土壤水流的模拟需要使用压头或土壤水分，或两者之间的切换，作为求解理查兹方程的主要变量。在非均质性、快速变化的大气边界或突然渗入干燥土壤等不利条件下，传统的非切换方法存在数值困难。由于数学复杂性，用主要变量切换方法解决这个问题不太受欢迎。虽然 Picard 方法因其简单性和稳定性而更适用于求解非切换模型，但两种不同形式的理查兹方程组合成一种数值方案，用于在特定水力条件下进行切换。该方法在通过 Picard 迭代方案求解的一维模型中成功实现。基于土壤水分保持关系的阈值饱和度用于在任一形式的理查兹方程之间切换。这里开发的方法适用于模拟非均质土壤中可变饱和的地下流动。与传统方法相比，所提出的模型质量守恒性好，数值上更加稳定和高效。