模拟地下水流运动的三重尺度有限元模型

谢一凡; 谢镇泽; 吴吉春; 张蔚; 谢春红; 鲁春辉

doi:10.11779/CJGE202211014

模拟地下水流运动的三重尺度有限元模型 English Version

谢一凡^{1, 2,},
谢镇泽^{1, 2},
吴吉春³,
张蔚⁴,
谢春红⁵,
鲁春辉^{1, 2, 6, ,}

1.
河海大学水文水资源与水利工程科学国家重点实验室, 江苏南京 210098
2.
河海大学水利水电学院, 江苏南京 210098
3.
南京大学地球科学与工程学院, 江苏南京 210023
4.
浙江省环境科技有限公司, 浙江杭州 310012
5.
南京大学数学系, 江苏南京 210093
6.
河海大学长江保护与绿色发展研究院, 江苏南京 210098

基金项目:

国家重点研发计划 2021YFC3200500

中央高校基本业务费项目 B210202018

国家自然科学基金面上项目 4227071940

详细信息

作者简介:
谢一凡(1987—)，男，副教授，博士，主要从事地下水数值算法的研究。E-mail: yfxie@hhu.edu.cn

通讯作者:
鲁春辉, Email：clu@hhu.edu.cn

中图分类号: TU43
计量
- 文章访问数: 167
- HTML全文浏览量: 52
- PDF下载量: 19
出版历程
- 收稿日期: 2021-10-24
- 网络出版日期: 2022-12-08
- 刊出日期: 2022-10-31

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

XIE Yi-fan^{1, 2,},
XIE Zhen-ze^{1, 2},
WU Ji-chun³,
ZHANG Wei⁴,
XIE Chun-hong⁵,
LU Chun-hui^{1, 2, 6, ,}

1.
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China
2.
College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China
3.
School of Earth Sciences and Engineering, Nanjing University, Nanjing 210023, China
4.
Zhejiang Environmental Technology Co., Ltd., Zhejiang 310012, China
5.
Department of Mathematics, Nanjing University, Nanjing 210093, China
6.
Yangtze Institute for Conservation and Development, Hohai University, Nanjing 210098, China

摘要

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。
- 地下水数值模拟 /
- 非均质 /
- 多尺度有限元法 /
- 基函数 /
- 超样本技术
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.
- numerical simulation of groundwater /
- heterogeneity /
- multiscale finite element method /
- basis function /
- over-sampling technique

HTML全文

研究区 $\mathit{\Omega}$ 剖分方式

Sketch map of subdivision of $\mathit{\Omega}$

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图 2 MSFEM粗网格剖分方式

Figure 2. Sketch map of standard subdivision of coarse element of MSFEM

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图 3 MSFEM-T粗网格剖分方式

Figure 3. Sketch map of standard subdivision of coarse element of MSFEM-T

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图 4 y=100 m处各数值方法水头绝对误差图

Figure 4. Absolute errors of hydraulic heads of different methods, with y=100 m

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图 5 不同放大倍数时水头绝对误差图

Figure 5. Absolute errors of hydraulic heads with different magnifications

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图 6 不同单元数时的计算用时和计算绝对误差图

Figure 6. CPU time and absolute errors of methods with different element numbers

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图 7 各数值方法在y=5000 m时的水头值

Figure 7. Calculated heads of different methods, with y=5000 m

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图 8 不同单元数时的计算用时和计算绝对误差图

Figure 8. CPU time and absolute errors of methods with different element numbers

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图 9 不同单元数时的基函数计算用时图

Figure 9. CPU time of basics function of MSFEM-L and MSFEM-T-L with different element numbers

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图 10 InK的方差为2和4时的分布图

Figure 10. InK fields of variance equal to 2 and 4

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图 11 各数值方法在y=5000 m处的水头相对误差图

Figure 11. Relative errors of hydraulic heads of different methods, with y=5000 m

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