TY - JOUR
T1 - Two-grid finite element method for the dual-permeability-Stokes fluid flow model
AU - Nasu, Nasrin Jahan
AU - Mahbub, Md Abdullah Al
AU - Hussain, Shahid
AU - Zheng, Haibiao
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/12
Y1 - 2021/12
N2 - 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.
AB - 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.
KW - Dual-permeability-Stokes system
KW - Horizontal wellbore
KW - Numerical experiments
KW - Two-grid algorithm
UR - https://www.scopus.com/pages/publications/85103596262
U2 - 10.1007/s11075-021-01091-z
DO - 10.1007/s11075-021-01091-z
M3 - 文章
AN - SCOPUS:85103596262
SN - 1017-1398
VL - 88
SP - 1703
EP - 1731
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 4
ER -