一种模拟节点达西流速的多尺度有限元-有限元模型  

Multiscale finite element-finite element model for simulating nodal Darcy velocity

作　　者：谢一凡 吴吉春[3] 王益 叶逾 谢春红[4] 鲁春辉 XIE Yi-fan;WU Ji-chun;WANG Yi;YE Yu;XIE Chun-hong;LU Chun-hui(State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,Hohai University,Nanjing 210024,China;College of Water Conservancy and Hydropower Engineering,Hohai University,Nanjing 210024,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 210024,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,江苏南京210024 [2]河海大学水利水电学院,江苏南京210024 [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,江苏南京210024

出　　处：《岩土工程学报》2022年第1期107-114,I0004,共9页Chinese Journal of Geotechnical 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);国家自然科学基金青年项目(41702243)。

摘　　要：提出了一种能高效模拟节点达西流速并保证其连续性的多尺度有限元-有限元模型(MSFEM-FEM)。该方法先应用多尺度有限元法(MSFEM)框架改进了Yeh的有限元模型的水头模拟部分以提升效率与精度,再将多尺度网格转化为有限元网格,应用Yeh的有限元框架保证流速的连续性。基于多尺度基函数,MSFEM-FEM能够汲取研究区的全局信息并在粗尺度上高效获得精确的水头解。通过将粗尺度网格转换为有限元网格,MSFEM-FEM能够应用Yeh的有限元框架将水头解中的全局信息导入达西流速,提高达西流速的精度并保证其连续性。在获得粗尺度解后,MSFEM-FEM还能应用多尺度基函数对解进行细尺度重构,从而获得研究区内的细尺度水头与流速。数值模拟结果显示MSFEM-FEM能够高效、精确的求解水头,并能够获得连续、精确的达西流速和流量。A multi-scale finite element-finite element model(MSFEM-FEM) is proposed,and it can effectively simulate the nodal Darcy velocity and ensure the velocity continuity.The MSFEM-FEM employs the multi-scale finite element method(MSFEM) to replace the head simulation part of the Yeh’s finite element model,thus to improve the efficiency and accuracy.Then,the MSFEM-FEM transforms the multi-scale grid to the finite element one,thus,it can directly apply the Yeh’s finite element model to obtain continuous Darcy velocity.Based on the multi-scale basis function,the MSFEM-FEM can extract the global information of the study area which allows it to obtain the accurate head solution efficiently on the coarse scale.By transforming the coarse-scale grid into the finite element grid,the MSFEM-FEM can directly employ the Yeh’s finite element model to import the global information from the head solution into the Darcy velocity,which can also improve the accuracy of Darcy velocity and ensure the velocity continuity.In addition,the MSFEM-FEM can apply multi-scale basis function to reconstruct the solutions,so as to obtain the fine-scale head and velocity solutions in the study area.The simulated results of two-dimensional groundwater problems show that the MSFEM-FEM can efficiently and accurately solve the head,Darcy velocity and flux,which outperforms the MSFEM and the Yeh’s finite element model.

关 键 词：地下水数值模拟 多尺度有限元法 Yeh的有限元模型 连续节点达西流速 高计算效率 

分 类 号：TU46[建筑科学—结构工程]