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Published August 15, 2019 | public
Journal Article

Multiresolution Operator Decomposition for Flow Simulation in Fractured Porous Media


Fractures should be simulated accurately given their significant effects on whole flow patterns in porous media. But such high-resolution simulations impose severe computational challenges to numerical methods in the applications. Therefore, the demand for accurate and efficient coarse-graining techniques is increasing. In this work, a near-linear complexity multiresolution operator decomposition method is proposed for solving and coarse graining flow problems in fractured porous media. We use the Discrete Fracture Model (DFM) to describe fractures, in which the fractures are explicitly represented as -dimensional elements. Using operator adapted wavelets, the solution space is decomposed into subspaces where DFM subsolutions can be computed by solving sparse and well-conditioned linear systems. By keeping only the coarse-scale part of the solution space, we furthermore obtain a reduced order model. We provide numerical experiments that investigate the accuracy of the reduced order model for different resolutions and different choices of medium.

Additional Information

© 2019 Published by Elsevier Inc. Received 8 November 2017, Revised 16 October 2018, Accepted 29 December 2018, Available online 9 January 2019. The authors gratefully acknowledge support from National Science and Technology Major Project (2016ZX05060-010), the Fundamental Research Funds for the Central Universities (17CX06007), HO and FS gratefully acknowledges this work supported by the Air Force Office of Scientific Research and the DARPA EQUiPS Program under award number FA9550-16-1-0054 (Computational Information Games) and the Air Force Office of Scientific Research under award number FA9550-18-1-0271 (Games for Computation and Learning).

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