1. 南京大学地球科学系，江苏 南京210093
• 收稿日期:2004-04-09 修回日期:2004-04-20 出版日期:2004-12-20
• 通讯作者: 叶淑君（1974-），女，湖北浠水人，讲师，主要从事水文地质、环境地质教学与科研工作. E-mail:E-mail：sjye@nju.edu.cn
• 基金资助:

国家自然科学基金项目“地面沉降条件下各向异性介质越流系统中水流模型研究”（编号：40172082）；国家自然科学基金重点项目“区域地面沉降模型研究”（编号：40335045）资助

### APPLICATION OF MULTISCALE FINITE ELEMENT METHOD TO THREE DIMENSIONAL GROUNDWATER FLOW PROBLEMS IN HETEROGENEOUS POROUS MEDIA

YE Shujun, WU Jichun, XUE Yuqun

1. Department of Earth Sciences, Nanjing University, Nanjing 210093, China
• Received:2004-04-09 Revised:2004-04-20 Online:2004-12-20 Published:2004-06-01

The multiscale finite element method (MsFEM) is applied to 3-D groundwater flow problems in heterogeneousporous media with different change in coefficients in the paper. The method can efficiently capture the large scale behavior of the solution without resolving all the small scale features by constructing the multiscale finite element base functions that are adaptive to the local property of the differential operator, which offers significant savings in CPU time and computer memory. The characteristic difference between MsFEM and the conventional finite element method(FEM) is attributed to base function. The base functions of MsFEM can indicate the variation of coefficients in an element, but those of the conventional FEM can't do it. The principle of the application of the multiscale finite element method to 3-D groundwater flow problems is introduced. Then two three dimensional groundwater flow problems in heterogeneous porous media are analyzed by the multiscale finite element method and the conventional finite element method, respectively. One is the 3-Dgroundwater flow problem with gradual change in coefficients in the horizontal direction and with abrupt change in the vertical direction. Another is the 3-Dgroundwater flow problem with the observation values of coefficients from the Borden test site. The solutions based on the MsFEM are much more accurate than those based on the conventional FEM with the same mesh size for the firstproblem with highly oscillatorycoefficients. The solutions based on the MsFEM are a littlemore accurate than those based on the conventional FEM with the same mesh size for the secondproblem with little change in coefficients. The applications demonstrate that the advantages of the multiscale finite element method for numerical simulation of 3-D groundwater flow in highly heterogeneous porous media, i.e. significantly reducing computational efforts, and improving the accuracy of the solutions, and that the multiscale finite element method for numerical simulation of 3-D groundwater flow in relative homogeneous porous media is effective but not obvious.

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