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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 575298, 19 pages
Research Article

New Scheme of Finite Difference Heterogeneous Multiscale Method to Solve Saturated Flow in Porous Media

Fulai Chen1,2 and Li Ren2

1Department of Mathematics, Xiangnan University, Chenzhou 423000, China
2Department of Soil and Water Sciences, China Agricultural University and Key Laboratory of Plant-Soil Interactions, MOE, Beijing 100094, China

Received 4 October 2013; Accepted 16 January 2014; Published 2 March 2014

Academic Editor: Shuyu Sun

Copyright © 2014 Fulai Chen and Li Ren. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new finite difference scheme, the development of the finite difference heterogeneous multiscale method (FDHMM), is constructed for simulating saturated water flow in random porous media. In the discretization framework of FDHMM, we follow some ideas from the multiscale finite element method and construct basic microscopic elliptic models. Tests on a variety of numerical experiments show that, in the case that only about a half of the information of the whole microstructure is used, the constructed scheme gives better accuracy at a much lower computational time than FDHMM for the problem of aquifer response to sudden change in reservoir level and gives comparable accuracy at a much lower computational time than FDHMM for the weak drawdown problem.