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

Authors

  • Maria Vasilyeva Institute for Scientific Computation, Texas A&M University, College Station, TX 77843-3368, USA
  • Eric T. Chung Department of Mathematics, The Chinese University of Hong Kong (CUHK), Hong Kong SAR
  • Yalchin Efendiev Department of Mathematics & Institute for Scientific Computation (ISC), Texas A&M University, College Station, Texas, USA
  • Aleksey Tyrylgin Multiscale Model Reduction Laboratory, North-Eastern Federal University, Yakutsk, Republic of Sakha (Yakutia), Russia, 677980

DOI:

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

Keywords:

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

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.

Published

2019-12-07

Issue

Section

Articles