Volume 27, Issue 2
A Three-Level Multi-Continua Upscaling Method for Flow Problems in Fractured Porous Media

Maria Vasilyeva, Eric T. Chung, Yalchin Efendiev & Aleksey Tyrylgin

Commun. Comput. Phys., 27 (2020), pp. 619-638.

Published online: 2019-12

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65N08, 65N30, 65M22

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

vasilyevadotmdotv@gmail.com (Maria Vasilyeva)

tschung@math.cuhk.edu.hk (Eric T. Chung)

efendiev@math.tamu.edu (Yalchin Efendiev)

koc9tk@mail.ru (Aleksey Tyrylgin)

  • BibTex
  • RIS
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@Article{CiCP-27-619, author = {Vasilyeva , Maria and Chung , Eric T. and Efendiev , Yalchin and Tyrylgin , Aleksey }, title = {A Three-Level Multi-Continua Upscaling Method for Flow Problems in Fractured Porous Media}, journal = {Communications in Computational Physics}, year = {2019}, volume = {27}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0219}, url = {http://global-sci.org/intro/article_detail/cicp/13461.html} }
TY - JOUR T1 - A Three-Level Multi-Continua Upscaling Method for Flow Problems in Fractured Porous Media AU - Vasilyeva , Maria AU - Chung , Eric T. AU - Efendiev , Yalchin AU - Tyrylgin , Aleksey JO - Communications in Computational Physics VL - 2 SP - 619 EP - 638 PY - 2019 DA - 2019/12 SN - 27 DO - http://dor.org/10.4208/cicp.OA-2018-0219 UR - https://global-sci.org/intro/article_detail/cicp/13461.html KW - Multiscale method, three-level scheme, multicontinuum, upscaling, GMsFEM, NLMC, fractured porous media. AB -

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.

Maria Vasilyeva, Eric T. Chung, Yalchin Efendiev & Aleksey Tyrylgin. (2019). A Three-Level Multi-Continua Upscaling Method for Flow Problems in Fractured Porous Media. Communications in Computational Physics. 27 (2). 619-638. doi:10.4208/cicp.OA-2018-0219
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