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A Two-Grid Decoupled Algorithm for a Multi-Dimensional Darcy–Brinkman Fracture Model

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Abstract

In this paper, we study numerical methods for solving a multi-dimensional fracture model, which couples n-dimensional Darcy flow in matrix with \((n-1)\)-dimensional Brinkman flow on fracture. A two-grid decoupled algorithm is proposed, in which the mixed model is decoupled by using the coarse grid approximation to the interface conditions, and then efficient single model solvers are applied for decoupled Darcy and Brinkman problems on the fine mesh. Error estimates show that the two-grid decoupled algorithm retains the same order of approximation accuracy as the coupled one. Numerical experiments in two-dimensional (2D) and three-dimensional (3D) geometries are conducted, and their results confirm our theoretical analysis to illustrate the efficiency and effectiveness of the proposed method for solving multi-domain problems.

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Authors and Affiliations

  1. Faculty of Science, Beijing University of Technology, Beijing, 100124, China

    Shuangshuang Chen, Qiumei Huang & Fei Xu

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  1. Shuangshuang Chen
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  2. Qiumei Huang
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  3. Fei Xu
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Correspondence to Qiumei Huang.

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The work of the first author was supported by Beijing Postdoctoral Foundation (zz2019-78). The work of the second author was supported by the National Nature Science Foundation of China Grant (11971047) and Beijing Natural Science Foundation Project (Z200002).

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Chen, S., Huang, Q. & Xu, F. A Two-Grid Decoupled Algorithm for a Multi-Dimensional Darcy–Brinkman Fracture Model. J Sci Comput 90, 88 (2022). https://doi.org/10.1007/s10915-021-01738-y

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  • DOI: https://doi.org/10.1007/s10915-021-01738-y

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