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谢一凡, 谢镇泽, 吴吉春, 张蔚, 谢春红, 鲁春辉. 模拟地下水流运动的三重尺度有限元模型[J]. 岩土工程学报, 2022, 44(11): 2081-2088. DOI: 10.11779/CJGE202211014
引用本文: 谢一凡, 谢镇泽, 吴吉春, 张蔚, 谢春红, 鲁春辉. 模拟地下水流运动的三重尺度有限元模型[J]. 岩土工程学报, 2022, 44(11): 2081-2088. DOI: 10.11779/CJGE202211014
XIE Yi-fan, XIE Zhen-ze, WU Ji-chun, ZHANG Wei, XIE Chun-hong, LU Chun-hui. Multiscale finite element method–triple grid model for simulation of groundwater flows[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(11): 2081-2088. DOI: 10.11779/CJGE202211014
Citation: XIE Yi-fan, XIE Zhen-ze, WU Ji-chun, ZHANG Wei, XIE Chun-hong, LU Chun-hui. Multiscale finite element method–triple grid model for simulation of groundwater flows[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(11): 2081-2088. DOI: 10.11779/CJGE202211014

模拟地下水流运动的三重尺度有限元模型

Multiscale finite element method–triple grid model for simulation of groundwater flows

  • 摘要: 传统有限元法在模拟地下水流问题时常需要精细剖分描述含水介质的非均质性以保证精度,导致计算消耗过高。传统多尺度有限元法(MSFEM)能缓解这一问题,但在处理高计算量问题时仍需较高消耗来构造基函数。提出了一种用于模拟地下水流的三重尺度有限元模型(MSFEM-T),该方法在MSFEM的粗、细两种尺度网格之间引入中网格,从而可以在粗网格单元内基于中、细两种尺度网格应用MSFEM本身替代有限元法构造基函数,能够显著降低基函数的构造消耗以提高整体计算效率。此外,MSFEM-T还提出了一种基于粗、中、细三重网格的超样本技术,可以进一步提升其计算精度。数值算例结果显示MSFEM-T的精度与MSFEM和精细剖分有限元法(LFEM-F)的精度相近,且计算效率更高。

     

    Abstract: The traditional finite element method often requires fine element grids to describle the heterogeneity of medium to ensure the accuracy for numerical modeling of groundwater, which leads to a large amount of calculation consumption. The multiscale finite element method can alleviate this problem, but it still needs a high cost to formulate the basis function when dealing with high computational complexity. A multiscale finite element method-triple grid model (MSFEM-T) is proposed for the simulation of groundwater flows. The MSFEM-T introduces an intermediate grid between the coarse grid and the fine grid, so that the basis function in the coarse grid can be established using the MSFEM instead of the FEM based on the intermediate and fine grids, therefore reducing the construction consumption of the basis function and improving the overall calculation efficiency. Moreover, the MSFEM-T uses an over-sampling method based on the coarse, intermediate and fine grids, which can further improve its calculation accuracy. The results show that the accuracy of the MSFEM-T is similar to that of the MSFEM and the finite element method of fine elements (LFEM-F), but the computational efficiency is much higher.

     

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