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Combination of multiscale finite element method and domain decomposition technique
for solving Darcian velocity in aquifers

1，2 3 1，2 4 1，2，5
XIE Yifan ，WU Jichun ，YE Yu ，XIE Chunhong ，LU Chunhui
（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. Department of Mathematics，Nanjing University，Nanjing 210093，China；
5. Yangtze Institute for Conservation and Development，Hohai University，Nanjing 210098，China）

Abstract：Groundwater aquifer is composed of many different geological materials. Darcy velocity at the in⁃
terface should conform to the refraction law，which is difficult to be accurately simulated by traditional nu⁃
merical methods. Therefore，this paper proposes a combination of the multi-scale finite element method and
domain decomposition method（MSFEM-D）， which can not only ensure the continuity of the vertical Darcy
velocity at the interface，but also ensure that the tangential Darcy velocity satisfies the refraction law，and
has high computational efficiency. The method employs multi-scale finite element method to simulate water
head to obtain global information so as to ensure the accuracy and to upscale the problem scale， thus to
reduce the calculation consumption. Then，the MSFEM-D uses the domain decomposition technology to sepa⁃
rate the media by material interface，and combines multi-scale basis function and Yeh's finite element mod⁃
el to effectively simulate Darcy velocity while ensuring the velocity continuity. Thus，the MSFEM-D can en⁃
sure that Darcy velocity satisfies the refraction law at material interfaces with high efficiency，while achiev⁃
ing a similar accuracy to the S 1 finite element model proposed by Zhou et al.
Keywords：groundwater numerical simulation；multiscale finite element method；domain decomposition tech⁃
nique；geological material interface；refraction law

（责任编辑：耿庆斋）

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