A dual-mesh multiscale finite element method for simulating nodal Darcy velocities in aquifers

ZHAO Wen-feng; XIE Yi-fan; WU Ji-chun

doi:10.11779/CJGE202008012

Volume 42 Issue 8

Turn off MathJax

Article Contents

Abstract

References

Chinese Journal of Geotechnical Engineering > 2020 > 42(8): 1474-1481. > DOI: 10.11779/CJGE202008012

ZHAO Wen-feng, XIE Yi-fan, WU Ji-chun. A dual-mesh multiscale finite element method for simulating nodal Darcy velocities in aquifers[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(8): 1474-1481. DOI: 10.11779/CJGE202008012

Citation:

PDF (1024 KB)

A dual-mesh multiscale finite element method for simulating nodal Darcy velocities in aquifers

1.
School of Earth Sciences and Engineering, Nanjing University, Nanjing 210023, China
2.
College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210024, China

More Information

Received Date: July 06, 2019
Available Online: December 05, 2022

Graphical Abstract

Abstract

Abstract

A dual-mesh multiscale finite element method (D-MSFEM) is developed to simulate nodal Darcy velocities in aquifers. It is a combination of the multiscale finite element method (MSFEM) and the dual-mesh finite element method (D-FEM). D-MSFEM can obtain continuous first-order head derivatives and solve the head and nodal Darcy velocities directly on the coarse grid without the necessity for solving Darcy equation specifically. Therefore, it breaks through the limitations of the traditional finite element basic framework and improves the computational efficiency extremely in comparison to the traditional methods for nodal Darcy velocities. D-MSFEM can also directly obtain the fine-scale nodal Darcy velocities by using the coarse-scale nodal Darcy velocities and the multiscale base functions, which can save a lot of computational cost. D-MSFEM is compared with some traditional methods for nodal Darcy velocities in the simulation of groundwater steady flow and transient flow. The results show that D-MSFEM achieves higher simulation efficiency and accuracy. This study may provide a new approach to simulate nodal Darcy velocities in aquifers efficiently.
- dual-mesh technique,
- multiscale finite element method,
- Darcy velocity,
- groundwater flow,
- numerical simulation

FullText(HTML)

References (20)

References

[1]	薛禹群, 谢春红. 地下水数值模拟[M]. 北京: 科学出版社, 2007: 175-178. XUE Yu-qun, XIE Chun-hong. Numerical simulation for Groundwater[M]. Beijing: Science Press, 2007: 175-178. (in Chinese)
[2]	ZHOU Q, BENSABAT J, BEAR J. Accurate calculation of specific discharge in heterogeneous porous media[J]. Water Resources Research, 2001, 37(12): 3057-3069. doi: 10.1029/1998WR900105
[3]	王铁行, 罗扬, 张辉. 黄土节理二维稳态流流量方程[J]. 岩土工程学报, 2013, 35(6): 1115-1120. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201306019.htm WANG Tie-hang, LUO Yang, ZHANG Hui. Two-dimensional steady flow rate equation for loess joints[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(6): 1115-1120. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201306019.htm
[4]	WOUTER Z. Finite-Element methods based on a transport velocity representation for groundwater motion[J]. Water Resources Research, 1984, 20(1): 137-145. doi: 10.1029/WR020i001p00137
[5]	谢一凡, 吴吉春, 薛禹群, 等. 一种模拟非均质介质中地下水流运动的快速提升尺度法[J]. 水利学报, 2015, 46(8): 918-924. doi: 10.13243/j.cnki.slxb.20141475 XIE Yi-fan, WU Ji-chun, XUE Yu-qun, et al. A fast upscaling method for simulating groundwater flow in heterogeneous media[J]. Journal of Hydraulic Engineering, 2015, 46(8): 918-924. (in Chinese) doi: 10.13243/j.cnki.slxb.20141475
[6]	EFENDIEV Y R, WU X H. Multiscale finite element for problems with highly oscillatory coefficients[J]. Numerische Mathematik, 2002, 90(3): 459-486. doi: 10.1007/s002110100274
[7]	薛禹群, 叶淑君, 谢春红, 等. 多尺度有限元法在地下水模拟中的应用[J]. 水利学报, 2004, 35(7): 7-13. doi: 10.3321/j.issn:0559-9350.2004.07.002 XUE Yu-qun, YE Shu-jun, XIE Chun-hong, et al. Application of multi-scale finite element method to simulation of groundwater flow[J]. Journal of Hydraulic Engineering, 2004, 35(7): 7-13. (in Chinese) doi: 10.3321/j.issn:0559-9350.2004.07.002
[8]	HOU T Y, WU X H. A multiscale finite element method for elliptic problems in composite materials and porous media[J]. Journal of Computational Physics, 1997, 134(1): 169-189. doi: 10.1006/jcph.1997.5682
[9]	YE S, XUE Y, XIE C. Application of the multiscale finite element method to flow in heterogeneous porous media[J]. Developments in Water Science, 2004, 55(9): 337-348.
[10]	贺新光, 任理. 求解非均质多孔介质中非饱和水流问题的一种自适应多尺度有限元方法——Ⅰ.数值格式[J]. 水利学报, 2009, 40(1): 38-45. doi: 10.13243/j.cnki.slxb.2009.01.017 HE Xin-guang, REN Li. Adaptive multiscale finite element method for unsaturated flow in heterogeneous porous media: I numerical scheme[J]. Journal of Hydraulic Engineering, 2009, 40(1): 38-45. (in Chinese) doi: 10.13243/j.cnki.slxb.2009.01.017
[11]	贺新光, 任理. 求解非均质多孔介质中非饱和水流问题的一种自适应多尺度有限元方法——Ⅱ.数值结果[J]. 水利学报, 2009, 40(2): 138-144. doi: 10.3321/j.issn:0559-9350.2009.02.002 HE Xin-guang, REN Li. Adaptive multiscale finite element method for unsaturated flow in heterogeneous porous media: II numerical result[J]. Journal of Hydraulic Engineering, 2009, 40(2): 138-144. (in Chinese) doi: 10.3321/j.issn:0559-9350.2009.02.002
[12]	叶淑君, 吴吉春, 薛禹群. 多尺度有限单元法求解非均质多孔介质中的三维地下水流问题[J]. 地球科学进展, 2004, 19(3): 437-442. https://www.cnki.com.cn/Article/CJFDTOTAL-DXJZ200403014.htm YE Shu-jun, WU Ji-chun, XUE Yu-qun. Application of multiscale finite element method to three dimensional groundwater flow problems in heterogeneous porous media[J]. Advance in Earth Sciences, 2004, 19(3): 437-442. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-DXJZ200403014.htm
[13]	于军, 吴吉春, 叶淑君, 等. 苏锡常地区非线性地面沉降耦合模型研究[J]. 水文地质工程地质, 2007(5): 11-16. doi: 10.16030/j.cnki.issn.1000-3665.2007.05.017 YU Jun, WU Ji-chun, YE Shu-jun, et al. Research on nonlinear coupled modeling of land subsidence in Suzhou, Wuxi and Changzhou areas, China[J]. Hydrogeology & Engineering Geology, 2007(5): 11-16. (in Chinese) doi: 10.16030/j.cnki.issn.1000-3665.2007.05.017
[14]	谢一凡, 吴吉春, 薛禹群, 等. 一种模拟节点达西渗透流速的三次样条多尺度有限单元法[J]. 岩土工程学报, 2015, 37(9): 1727-1732. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201509030.htm XIE Yi-fan, WU Ji-chun, XUE Yu-qun, et al. A cubic-spline multiscale finite element method for simulating nodal Darcy velocities[J]. Chinese Journal of Geotechnical Engineering, 2015, 37(9): 1727-1732. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201509030.htm
[15]	谢一凡, 吴吉春, 薛禹群, 等. 结合有限单元法运用三次样条技术求解达西渗透流速[J]. 水文地质工程地质, 2015, 42(5): 1-5. XIE Yi-fan, WU Ji-chun, XUE Yu-qun, et al. Combination of finite element method and cubic-spline technique to solve Darcy velocities[J]. Hydrogeology & Engineering Geology, 2015, 42(5): 1-5. (in Chinese)
[16]	XIE Y, WU J, XIE C. Cubic-spline multiscale finite element method for solving nodal Darcian velocities in porous media[J]. Journal of Hydrologic Engineering, 2015, 20(11): 04015030. doi: 10.1061/(ASCE)HE.1943-5584.0001222
[17]	谢一凡. 改进多尺度有限单元法求解二维地下水流问题[D]. 南京: 南京大学, 2015. XIE Yi-fan, Improved Multiscale Finite Element Method for Solving Two-Dimensional Groundwater Flow Problems[D]. Nanjing: Nanjing University, 2015. (in Chinese)
[18]	XIE Y F, WU J C, XUE Y Q, et al Combination of multiscale finite-element method and Yeh's finite-element model for solving nodal Darcian velocities and fluxesin porous media[J]. Journal of Hydrologic Engineering, 2016, 21(12): 04016048. doi: 10.1061/(ASCE)HE.1943-5584.0001456
[19]	VEDAT B. A finite element dual mesh method to calculate Nodal Darcy velocities in nonhomogeneous and anisotropic aquifers[J]. Water Resources Research, 1984, 20(11): 1705-1717. doi: 10.1029/WR020i011p01705
[20]	YEH G T. On the computation of Darcian velocity and mass balance in the finite element modeling of groundwater flow[J]. Water Resources Research, 1981, 17(5): 1529-1534. doi: 10.1029/WR017i005p01529