Journal of Applied Mathematics
Volume 2011 (2011), Article ID 861905, 24 pages
Research Article

Multiscale Time-Splitting Strategy for Multiscale Multiphysics Processes of Two-Phase Flow in Fractured Media

1Computational Transport Phenomena Laboratory, Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
2Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum, Beijing 102249, China

Received 15 December 2010; Accepted 8 January 2011

Academic Editor: Zhangxin Chen

Copyright © 2011 Jisheng Kou 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.


The temporal discretization scheme is one important ingredient of efficient simulator for two-phase flow in the fractured porous media. The application of single-scale temporal scheme is restricted by the rapid changes of the pressure and saturation in the fractured system with capillarity. In this paper, we propose a multi-scale time splitting strategy to simulate multi-scale multi-physics processes of two-phase flow in fractured porous media. We use the multi-scale time schemes for both the pressure and saturation equations; that is, a large time-step size is employed for the matrix domain, along with a small time-step size being applied in the fractures. The total time interval is partitioned into four temporal levels: the first level is used for the pressure in the entire domain, the second level matching rapid changes of the pressure in the fractures, the third level treating the response gap between the pressure and the saturation, and the fourth level applied for the saturation in the fractures. This method can reduce the computational cost arisen from the implicit solution of the pressure equation. Numerical examples are provided to demonstrate the efficiency of the proposed method.