Abstract
In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 7851-7868 |
| Number of pages | 18 |
| Journal | Water Resources Research |
| Volume | 52 |
| Issue number | 10 |
| DOIs | |
| State | Published - Oct 12 2016 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): BAS/1/1351-01-01
Acknowledgements: The authors would like to thank the anonymous reviewers for their insightful comments and suggestions that have contributed to improve this paper. No data were used in producing this manuscript, except in the fourth case of Example 5.1, where the data from the 10th SPE Comparative Solution Project on Upscaling (available at http://www.spe.org/web/csp/) were used. The work of H. Chen was supported by the NSF of China (grant 11201394) and the Fundamental Research Funds for the Central Universities (grant 20720150005). The work of S. Sun was supported by King Abdullah University of Science and Technology (KAUST) through the grant BAS/1/1351-01-01.