Determining the temperature and water content of soil, at a given instant or along time, is fundamental to understand several soil‐related phenomena and processes. Evaporation, aeration, chemical‐reaction rates and types, biological processes such as germination and growth of seeds, root development, nutrient and water uptake by roots, and decomposition of organic matter by microbes, are all strongly influenced by soil temperature. On the other hand, infiltration of water through the soil surface allows soil to temporarily store water, making it available for uptake by plants and organisms living in soil. Furthermore, soil water content is closely related to physical and chemical properties of soil, such as oxygen content and demand, which impacts root breathing, microbial activity and soil chemical balance. The accurate evaluation of these two parameters and their interconnection is even relevant in semi‐arid regions, where climate conditions are particularly difficult, such as the north‐eastern zone of Brazil. Thus, the use of computational models and coupled approaches are imperative for rigorous descriptions. This work presents a contribution to estimate soil temperature and water content, by solving the heat transfer equation and the Richards equation, respectively, through finite differences. As input, the model uses the experimental material composition of the soil, the time‐dependent temperature profile at the surface and information about the regional rain regime. Three different numerical approaches were implemented: explicit, simple implicit and the Crank–Nicolson method. The calculations for temperature and water content of the soil obtained with these computational models were compared with the results from Computational Fluid Dynamics (CFD). The relative differences between the numerical methods were less than 0.006% by solving the heat transfer equation and less than 2.75% using the Richards equation. The maximum relative differences within the model, including both a constant and a variable water‐content profile, were 3.28%. The results from the computational model using the CFX tool have maximum relative differences of 0.6%, which contributes to verifying the accuracy of the implemented methods.

中文翻译：

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使用有限差分和 CFD 估算巴西半干旱地区土壤温度和含水量


确定给定时刻或一段时间内土壤的温度和含水量对于理解一些与土壤相关的现象和过程至关重要。蒸发、通气、化学反应速率和类型、生物过程（例如种子的发芽和生长、根部发育、根部吸收养分和水分以及微生物对有机物的分解）都受到土壤温度的强烈影响。另一方面，水通过土壤表面的渗透使土壤能够暂时储存水，使其可供生活在土壤中的植物和生物体吸收。此外，土壤含水量与土壤的含氧量和需氧量等理化性质密切相关，影响根系呼吸、微生物活动和土壤化学平衡。对这两个参数及其相互关系的准确评估甚至适用于气候条件特别困难的半干旱地区，例如巴西东北部地区。因此，计算模型和耦合方法的使用对于严格的描述是必要的。这项工作通过有限差分分别求解传热方程和理查兹方程，为估计土壤温度和含水量做出了贡献。该模型使用土壤的实验材料成分、地表随时间变化的温度分布以及有关区域降雨状况的信息作为输入。实施了三种不同的数值方法：显式方法、简单隐式方法和克兰克-尼科尔森方法。将使用这些计算模型获得的土壤温度和含水量计算结果与计算流体动力学 (CFD) 的结果进行比较。 通过求解传热方程，数值方法之间的相对差异小于0.006%；通过求解Richards方程，数值方法之间的相对差异小于2.75%。模型内的最大相对差异（包括恒定和可变的含水量曲线）为 3.28%。使用CFX工具计算模型的结果最大相对差异为0.6%，这有助于验证所实施方法的准确性。