Abstract
In this paper, we are interested in an efficient numerical method for the mixed-dimensional approach to modeling single-phase flow in fractured porous media. The model introduces fractures and their intersections as lower-dimensional structures, and the mortar variable is used for flow coupling between the matrix and fractures. We consider a stable mixed finite element discretization of the problem, which results in a parameter-dependent linear system. For this, we develop block preconditioners based on the well-posedness of the discretization choice. The preconditioned iterative method demonstrates robustness with regard to discretization and physical parameters. The analytical results are verified on several examples of fracture network configurations, and notable results in reduction of number of iterations and computational time are obtained.
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Acknowledgments
A special thanks is extended to James Adler, Alessio Fumagalli and Eirik Keilegavlen for valuable comments and discussions on the presented work. The authors also would like to thank Casey Cavanaugh for improving the style of the presentation.
Funding
Open Access funding provided by University of Bergen. The first author acknowledges the financial support from the TheMSES project funded by Norwegian Research Council grant 250223. The work of the second author is partially supported by the National Science Foundation under grant DMS-1620063.
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Budiša, A., Hu, X. Block preconditioners for mixed-dimensional discretization of flow in fractured porous media. Comput Geosci 25, 671–686 (2021). https://doi.org/10.1007/s10596-020-09984-z
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DOI: https://doi.org/10.1007/s10596-020-09984-z
Keywords
- Porous medium
- Fracture flow
- Mixed finite element
- Algebraic multigrid method
- Iterative method
- Preconditioning