Nonlocal multicontinua upscaling for multicontinua flow problems in fractured porous media
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AbstractOur goal of this paper is to develop a new upscaling method for multicontinua flow problems in fractured porous media. We consider a system of equations that describes flow phenomena with multiple flow variables defined on both matrix and fractures. To construct our upscaled model, we will apply the nonlocal multicontinua (NLMC) upscaling technique. The upscaled coefficients are obtained by using some multiscale basis functions, which are solutions of local problems defined on oversampled regions. For each continuum within a target coarse element, we will solve a local problem defined on an oversampling region obtained by extending the target element by few coarse grid layers, with a set of constraints which enforce the local solution to have mean value one on the chosen continuum and zero mean otherwise. The resulting multiscale basis functions have been shown to have good approximation properties. To illustrate the idea of our approach, we will consider a dual continua background model consisting of discrete fractures in two space dimensions, that is, we consider a system with three continua. We will present several numerical examples, and they show that our method is able to capture the interaction between matrix continua and discrete fractures on the coarse grid efficiently.
All Author(s) ListMaria Vasilyeva, Eric T. Chung, Siu Wun Cheung, Yating Wang, Georgy Prokopev
Journal nameJournal of Computational and Applied Mathematics
Year2019
Month8
Day1
Volume Number355
Pages258 - 267
ISSN0377-0427
eISSN1879-1778
LanguagesEnglish-United States

Last updated on 2020-05-08 at 01:22