A robust, high order modeling approach is introduced, based on the finite difference-based radial basis functions method, for solving the groundwater flow equation in the presence of an active well, in the case of a confined aquifer in a complex geological environment. The two important novelties of this work are the analytical handling of the wells’ singularities and the ability to do this accurately and efficiently in a heterogeneous medium. It is argued that the most commonly used methods for this type of problem have severe weaknesses in both the treatment of the singularities associated with the well, and in representing heterogeneities which commonly occur in geological processes. The method presented here is first applied to the groundwater flow problem in a homogeneous medium for which the analytical solution is known, to show its high order algebraic convergence. The method is then compared against the United States geological survey’s MODFLOW software on a quasi-realistic benchmark test case in a heterogeneous medium. It is shown that much fewer nodes are needed by the proposed method to yield a similar accuracy.

中文翻译：

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非均质系统中地质过程数值逼近的径向基函数方法

在基于有限差分的径向基函数方法的基础上，引入了一种鲁棒的高阶建模方法，用于在复杂地质环境中受限含水层的情况下，在有活动井的情况下求解地下水流方程。这项工作的两个重要新颖之处是对井的奇异性的分析处理以及在异质介质中准确有效地进行处理的能力。有人认为，最常见的解决这类问题的方法在处理与井相关的奇异性和表示地质过程中常见的异质性方面都存在严重的弱点。这里介绍的方法首先应用于已知分析溶液的均质介质中的地下水流动问题，显示其高阶代数收敛。然后将该方法与美国地质调查局的MODFLOW软件在异构介质上的准真实基准测试用例上进行比较。结果表明，所提出的方法需要更少的节点来产生相似的精度。