The unsaturated zone profoundly affects groundwater (GW) flow induced by pumping and injection due to the capillary forces. However, current radial basis function (RBF) numerical models for GW pumping and injection mostly ignore the unsaturated zone. To bridge this gap, we developed a new three-dimensional weak strong form RBF model in this study, called CCHE3D-GW-RBF. Flow processes were modelled by the mixed-form Richards equation which was iteratively solved by the modified Picard iteration. Soil-water characteristic curves were represented by the widely applicable formulas, the van Genuchten (1980) model. Differential operators were approximated by the localized Gaussian RBF, and the weighted singular value decomposition method was used to construct stable bases. The injection/pumping wells and the flux boundaries were handled by the weak formulation using Meshless Local Petrov Galerkin method, and the strong-form equation using the collocation RBF method was enforced on the other points. Good agreement was found between the simulation results from our numerical model and the well-accepted solutions in all three verification cases, demonstrating the accuracy and applicability of this model. In addition, a smaller RBF shape parameter was found to produce a more accurate modelling resulting, indicating the necessity of implementing stable bases for RBF models.

中文翻译：

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一种稳定的局部弱强式径向基函数方法，用于模拟抽水和注入引起的可变饱和地下水流


由于毛细管力，非饱和区深刻影响抽水和注入引起的地下水（GW）流量。然而，当前的GW泵送和注入的径向基函数（RBF）数值模型大多忽略了非饱和区。为了弥补这一差距，我们在本研究中开发了一种新的三维弱强形式 RBF 模型，称为 CCHE3D-GW-RBF。流动过程通过混合形式的理查兹方程进行建模，该方程通过改进的皮卡德迭代进行迭代求解。土壤-水特征曲线由广泛适用的公式表示，即van Genuchten (1980)模型。微分算子采用局域高斯RBF逼近，并采用加权奇异值分解方法构造稳定基。注/抽油井和通量边界采用无网格局部 Petrov Galerkin 方法的弱公式处理，并在其他点上采用搭配 RBF 方法的强形式方程。在所有三个验证案例中，我们的数值模型的模拟结果与公认的解决方案之间存在良好的一致性，证明了该模型的准确性和适用性。此外，发现较小的 RBF 形状参数可以产生更准确的建模结果，这表明有必要为 RBF 模型实现稳定的基础。