Robin-Robin domain decomposition methods for the dual-porosity-conduit system

The recently developed dual-porosity-Stokes model describes a complicated dual-porosity-conduit system which uses a dual-porosity/permeability model to govern the flow in porous media coupled with free flow via four physical interface conditions. This system has important applications in unconventio...

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Bibliographic Details
Published in:Advances in computational mathematics 2021-02, Vol.47 (1), Article 7
Main Authors: Hou, Jiangyong, Yan, Wenjing, Hu, Dan, He, Zhengkang
Format: Article
Language:English
Subjects:
Algorithms
Boundary conditions
Computational fluid dynamics
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Convergence
Decomposition
Domain decomposition methods
Free flow
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Porosity
Porous media
Visualization
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Summary:The recently developed dual-porosity-Stokes model describes a complicated dual-porosity-conduit system which uses a dual-porosity/permeability model to govern the flow in porous media coupled with free flow via four physical interface conditions. This system has important applications in unconventional reservoirs especially the multistage fractured horizontal wellbore problems. In this paper, we propose and analyze domain decomposition methods to decouple the large system arisen from the discretization of dual-porosity-Stokes model. Robin boundary conditions are used to decouple the coupling conditions on the interface. Then, Robin-Robin domain decomposition methods are constructed based on the two decoupled sub-problems. Convergence analysis is demonstrated and a geometric convergence order is obtained. Optimized Schwarz methods are proposed for the dual-porosity-Stokes model and optimized Robin parameters are obtained to improve the convergence of proposed algorithms. Three computational experiments are presented to illustrate and validate the accuracy and applicability of proposed algorithms.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-020-09828-5