A Three-Level Multi-Continua Upscaling Method for Flow Problems in Fractured Porous Media

A Three-Level Multi-Continua Upscaling Method for Flow Problems in Fractured Porous Media

Year:    2020

Author:    Maria Vasilyeva, Eric T. Chung, Yalchin Efendiev, Aleksey Tyrylgin

Communications in Computational Physics, Vol. 27 (2020), Iss. 2 : pp. 619–638

Abstract

Traditional two level upscaling techniques suffer from a high offline cost when the coarse grid size is much larger than the fine grid size one. Thus, multilevel methods are desirable for problems with complex heterogeneities and high contrast. In this paper, we propose a novel three-level upscaling method for flow problems in fractured porous media. Our method starts with a fine grid discretization for the system involving fractured porous media. In the next step, based on the fine grid model, we construct a nonlocal multi-continua upscaling (NLMC) method using an intermediate grid. The system resulting from NLMC gives solutions that have physical meaning. In order to enhance locality, the grid size of the intermediate grid needs to be relatively small, and this motivates using such an intermediate grid. However, the resulting NLMC upscaled system has a relatively large dimension. This motivates a further step of dimension reduction. In particular, we will apply the idea of the Generalized Multiscale Finite Element Method (GMsFEM) to the NLMC system to obtain a final reduced model. We present simulation results for a two-dimensional model problem with a large number of fractures using the proposed three-level method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2018-0219

Communications in Computational Physics, Vol. 27 (2020), Iss. 2 : pp. 619–638

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Multiscale method three-level scheme multicontinuum upscaling GMsFEM NLMC fractured porous media.

Author Details

Maria Vasilyeva

Eric T. Chung

Yalchin Efendiev

Aleksey Tyrylgin