The main purpose of this study is to develop a numerical model of unsaturated flow in soils with plant root water uptake. The Richards equation and different sink term formulations are used in the numerical model to describe the distribution of soil moisture in the root zone. The Kirchhoff transformed Richards equation is used and the Gardner model is considered for capillary pressure. In the proposed numerical approach, we used localized radial basis function (LRBF) meshless techniques in space and the backward Euler scheme for temporal discretization to solve the system. The LRBF approach is an accurate and computationally efficient method that does not require mesh generation and is flexible in addressing high-dimensional problems. Furthermore, this method leads to a sparse matrix system, which avoids ill-conditioning issues. We implement the numerical model of infiltration and plant root water uptake for one, two, and three-dimensional soils. Numerical experiments are performed using nontrivial analytical solutions and available experimental data to validate the performance of the proposed numerical techniques. The results demonstrate the capability of the proposed numerical model to predict soil moisture dynamics in root zone.

中文翻译：

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用于预测根区土壤水分分布的 LRBF 无网格方法


本研究的主要目的是开发具有植物根系水分吸收的土壤中非饱和流的数值模型。在数值模型中使用 Richards 方程和不同的汇项公式来描述根区土壤水分的分布。使用 Kirchhoff 变换的 Richards 方程，并考虑使用 Gardner 模型计算毛细管压力。在提出的数值方法中，我们在空间中使用了局部径向基函数 （LRBF） 无网格技术和用于时间离散化的向后欧拉方案来求解系统。LRBF 方法是一种精确且计算高效的方法，不需要生成网格，并且在解决高维问题方面非常灵活。此外，这种方法导致了稀疏矩阵系统，从而避免了病态问题。我们对一维、二维和三维土壤实施了渗透和植物根系水分吸收的数值模型。使用非平凡的解析解和可用的实验数据进行数值实验，以验证所提出的数值技术的性能。结果表明，所提出的数值模型能够预测根区土壤水分动态。