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Open AccessArticle

Mixed Generalized Multiscale Finite Element Method for Darcy-Forchheimer Model

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Multiscale Model Reduction Laboratory, North-Eastern Federal University, 677980 Yakutsk, Republic of Sakha (Yakutia), Russia
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School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
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Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan 411105, China
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Key Laboratory of Intelligent Computing Information Processing of Ministry of Education, Xiangtan 411105, China
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Institute for Scientific Computation, Texas A&M University, College Station, TX 77843-3368, USA
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Department of Computational Technologies, North-Eastern Federal University, 677980 Yakutsk, Republic of Sakha (Yakutia), Russia
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Department of Mathematics, The Chinese University of Hong Kong (CUHK), Hong Kong, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1212; https://doi.org/10.3390/math7121212
Received: 7 October 2019 / Revised: 3 December 2019 / Accepted: 5 December 2019 / Published: 10 December 2019
(This article belongs to the Special Issue Computational Mathematics, Algorithms, and Data Processing)
In this paper, the solution of the Darcy-Forchheimer model in high contrast heterogeneous media is studied. This problem is solved by a mixed finite element method (MFEM) on a fine grid (the reference solution), where the pressure is approximated by piecewise constant elements; meanwhile, the velocity is discretized by the lowest order Raviart-Thomas elements. The solution on a coarse grid is performed by using the mixed generalized multiscale finite element method (mixed GMsFEM). The nonlinear equation can be solved by the well known Picard iteration. Several numerical experiments are presented in a two-dimensional heterogeneous domain to show the good applicability of the proposed multiscale method. View Full-Text
Keywords: Darcy-Forchheimer model; flow in porous media; nonlinear equation; heterogeneous media; finite element method; multiscale method; mixed generalized multiscale finite element method; multiscale basis functions; two-dimensional domain Darcy-Forchheimer model; flow in porous media; nonlinear equation; heterogeneous media; finite element method; multiscale method; mixed generalized multiscale finite element method; multiscale basis functions; two-dimensional domain
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MDPI and ACS Style

Spiridonov, D.; Huang, J.; Vasilyeva, M.; Huang, Y.; Chung, E.T. Mixed Generalized Multiscale Finite Element Method for Darcy-Forchheimer Model. Mathematics 2019, 7, 1212.

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