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Two-grid finite element method for the dual-permeability-Stokes fluid flow model

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Abstract

In this paper, two-grid finite element method for the steady dual-permeability-Stokes fluid flow model is proposed and analyzed. Dual-permeability-Stokes interface system has vast applications in many areas such as hydrocarbon recovery process, especially in hydraulically fractured tight/shale oil/gas reservoirs. Two-grid method is popular and convenient to solve a large multiphysics interface system by decoupling the coupled problem into several subproblems. Herein, the two-grid approach is used to reduce the coding task substantially, which provides computational flexibility without losing the approximate accuracy. Firstly, we solve a global problem through standard Pk − Pk− 1 − Pk − Pk finite elements on the coarse grid. After that, a coarse grid solution is applied for the decoupling between the interface terms and the mass exchange terms to solve three independent subproblems on the fine grid. The three independent parallel subproblems are the Stokes equations, the microfracture equations, and the matrix equations, respectively. Four numerical tests are presented to validate the numerical methods and illustrate the features of the dual-permeability-Stokes model.

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Funding

All authors are partially supported by NSF of China (Grant No. 11971174), NSF of Shanghai (Grant No. 19ZR1414300), and Science and Technology Commission of Shanghai Municipality (Grant No. 18dz2271000).

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  1. School of Mathematical Sciences and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, 200241, People’s Republic of China

    Nasrin Jahan Nasu, Md. Abdullah Al Mahbub, Shahid Hussain & Haibiao Zheng

  2. Department of Accounting, University of Chittagong, Chattogram, Bangladesh

    Nasrin Jahan Nasu

  3. Department of Mathematics, Comilla University, Cumilla, 3506, Bangladesh

    Md. Abdullah Al Mahbub

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  1. Nasrin Jahan Nasu
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Nasu, N.J., Mahbub, M.A.A., Hussain, S. et al. Two-grid finite element method for the dual-permeability-Stokes fluid flow model. Numer Algor 88, 1703–1731 (2021). https://doi.org/10.1007/s11075-021-01091-z

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