一种模拟介质交界面处达西流速的分区多尺度有限单元法  

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

作　　者：谢一凡 吴吉春[3] 叶逾 谢春红[4] 鲁春辉 XIE Yifan;WU Jichun;YE Yu;XIE Chunhong;LU Chunhui(State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,Hohai University,Nanjing 210098,China;College of Water Conservancy and Hydropower Engineering,Hohai University,Nanjing 210098,China;School of Earth Sciences and Engineering,Nanjing University,Nanjing 210023,China;Department of Mathematics,Nanjing University,Nanjing 210093,China;Yangtze Institute for Conservation and Development,Hohai University,Nanjing 210098,China)

机构地区：[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]南京大学数学系,江苏南京210093 [5]河海大学长江保护与绿色发展研究院,江苏南京210098

出　　处：《水利学报》2021年第8期979-988,共10页Journal of Hydraulic Engineering

基　　金：中央高校基本业务费项目(B210202018);国家自然科学基金面上项目(51879088)。

摘　　要：地下含水层常由多种不同含水介质组成,交界面处的达西流速需符合折射定律,传统数值方法难以准确模拟。基于多尺度有限元法和区域分解技术提出分区多尺度有限元法(Multiscale finite element method with Domain decomposition technique,MSFEM-D)模拟交界面处的达西流速。该方法运用多尺度有限元法模拟水头,获取全局信息保证解的精度,并提升尺度以降低计算消耗;再利用区域分解技术将研究区分区以分离界面两侧介质,同时结合多尺度基函数和Yeh的有限元模型来高效模拟达西流速。因此,MSFEM-D不仅能保证交界面处的法向达西流速的连续性,还能保证切向达西流速符合折射定律。数值模拟结果表明MSFEM-D能够保证达西流速在交界面处满足折射定律,精度与Zhou等的S1有限元模型相近,并可节约大量计算消耗。Groundwater aquifer is composed of many different geological materials.Darcy velocity at the interface should conform to the refraction law,which is difficult to be accurately simulated by traditional numerical 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 separate the media by material interface,and combines multi-scale basis function and Yeh's finite element model to effectively simulate Darcy velocity while ensuring the velocity continuity.Thus,the MSFEM-D can ensure that Darcy velocity satisfies the refraction law at material interfaces with high efficiency,while achieving a similar accuracy to the S1 finite element model proposed by Zhou et al.

关 键 词：地下水数值模拟 多尺度有限元法 区域分解技术 含水介质交界面 折射定律 

分 类 号：P641.2[天文地球—地质矿产勘探]