Three-dimensional local grid refinement for block-centered finite-difference groundwater models using iteratively coupled shared nodes: A new method of interpolation and analysis of errors
Three-dimensional local grid refinement for block-centered finite-difference groundwater models using iteratively coupled shared nodes: A new method of interpolation and analysis of errors
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DOI：
10.1016/j.advwatres.2004.06.004
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发表时间：
2004-09
影响因子：
4.7
通讯作者：
S. Mehl;M. Hill
中科院分区：
文献类型：
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作者：
S. Mehl;M. Hill
本文描述了将 Mehl 和 Hill 的块中心有限差分地下水模型的二维局部网格细化方法扩展到三维的工作 [使用共享节点的块中心有限差分地下水模型的局部网格细化方法的开发和评估。高级水资源 2002；25(5):497–511]。在这种方法中，（父）有限差分网格在（子）子区域内被更精细地离散化。网格细化方法顺序求解每个网格，并使用指定的通量（父）和指定的头（子）边界条件来耦合网格。迭代实现了两个网格的水头和通量之间的收敛。最值得关注的是如何将头部插值到子网格的边界上，以便在三个维度上保留父网格流的物理特性。我们开发了一种新的两步“笼壳”插值方法，该方法基于与父网格共享的节点之间的子边界上的流动方程的解。使用测试用例的误差分析表明，采用笼壳边界水头插值的共享节点局部网格细化方法是准确且稳健的，并且所得代码可用于研究河流-含水层相互作用的三维局部网格细化。结果表明，(1) 父网格和子网格相互作用，将真实的水头和通量解转移到两个网格的水头和通量处于平衡状态的不同解，(2) 局部细化模型为细化区域中的水头和通量提供了一个解，只有在执行迭代以使水头和通量都处于平衡的情况下，该模型才比未细化的模型更准确，以及 (3) 精度 耦合的大小受到父网格大小的限制 - 粗略的父网格限制了子网格反馈中水力学的正确表示。
This paper describes work that extends to three dimensions the two-dimensional local-grid refinement method for block-centered finite-difference groundwater models of Mehl and Hill [Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes. Adv Water Resour 2002;25(5):497–511]. In this approach, the (parent) finite-difference grid is discretized more finely within a (child) sub-region. The grid refinement method sequentially solves each grid and uses specified flux (parent) and specified head (child) boundary conditions to couple the grids. Iteration achieves convergence between heads and fluxes of both grids. Of most concern is how to interpolate heads onto the boundary of the child grid such that the physics of the parent-grid flow is retained in three dimensions. We develop a new two-step, “cage-shell” interpolation method based on the solution of the flow equation on the boundary of the child between nodes shared with the parent grid. Error analysis using a test case indicates that the shared-node local grid refinement method with cage-shell boundary head interpolation is accurate and robust, and the resulting code is used to investigate three-dimensional local grid refinement of stream-aquifer interactions. Results reveal that (1) the parent and child grids interact to shift the true head and flux solution to a different solution where the heads and fluxes of both grids are in equilibrium, (2) the locally refined model provided a solution for both heads and fluxes in the region of the refinement that was more accurate than a model without refinement only if iterations are performed so that both heads and fluxes are in equilibrium, and (3) the accuracy of the coupling is limited by the parent-grid size—a coarse parent grid limits correct representation of the hydraulics in the feedback from the child grid.