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Multiresolution Operator Decomposition for Flow Simulation in Fractured Porous Media

Zhang, Qingfu and Owhadi, Houman and Yao, Jun and Schäfer, Florian and Huang, Zhaoqin and Li, Yang (2019) Multiresolution Operator Decomposition for Flow Simulation in Fractured Porous Media. Journal of Computational Physics, 391 . pp. 381-396. ISSN 0021-9991.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription
Owhadi, Houman0000-0002-5677-1600
Li, Yang0000-0002-4939-8174
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).
Funding AgencyGrant Number
National Science and Technology Major Project2016ZX05060-010
Fundamental Research Funds for the Central Universities17CX06007
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0054
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-18-1-0271
Subject Keywords:Multigrid method; Discrete fracture model; Flow simulation; Fractured porous media; Multiresolution decomposition
Record Number:CaltechAUTHORS:20190109-090349439
Persistent URL:
Official Citation:Qingfu Zhang, Houman Owhadi, Jun Yao, Florian Schäfer, Zhaoqin Huang, Yang Li, Multiresolution operator decomposition for flow simulation in fractured porous media, Journal of Computational Physics, Volume 391, 2019, Pages 381-396, ISSN 0021-9991, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92155
Deposited By: Tony Diaz
Deposited On:09 Jan 2019 18:30
Last Modified:09 Mar 2020 13:19

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