`ISRN Applied MathematicsVolume 2012, Article ID 202893, 10 pageshttp://dx.doi.org/10.5402/2012/202893`
Research Article

## A Combination Method of Mixed Multiscale Finite-Element and Laplace Transform for Flow in a Dual-Permeability System

1CAS Key Laboratory of Marginal Sea Geology, South China Sea Institute of Oceanology, Guangzhou 510301, China
2Graduate University, CAS, Beijing 100049, China
3Faculty of Science, East China Institute of Technology, Fuzhou 344000, China

Received 28 April 2012; Accepted 28 May 2012

Academic Editors: H. Du and G. Kyriacou

Copyright © 2012 Tang-Wei Liu et al. 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.

#### Abstract

An efficient combination method of Laplace transform and mixed multiscale finite-element method for coupling partial differential equations of flow in a dual-permeability system is present. First, the time terms of parabolic equation with unknown pressure term are removed by the Laplace transform. Then the transformed equations are solved by mixed FEMs which can provide the numerical approximation formulas for pressure and velocity at the same time. With some assumptions, the multiscale basis functions are constructed by utilizing the effects of fine-scale heterogeneities through basis functions formulation computed from local flow problems. Without time step in discrete process, the present method is efficient when solving spatial discrete problems. At last, the associated pressure transform is inverted by the method of numerical inversion of the Laplace transform.