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A Multi-grid Decoupling Method for the Coupled Fluid Flow with the Porous Media Flow

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Abstract

In this paper, we propose a multi-grid decoupling method for the coupled Navier–Stokes–Darcy problem with the Beavers–Joseph–Saffman interface condition. The basic idea of the method is to first solve a much smaller global problem on a very coarse initial grid, then solve a linearized Newton problem and a Darcy problem in parallel on all the subsequently refined grids. Error bounds of the approximate solution for the proposed method are analyzed, and optimal error estimates are obtained. Numerical experiments are conducted to verify the theoretical analysis and indicate the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Jinan, Jinan, 250022, China

    Liyun Zuo

  2. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Guangzhi Du

Authors
  1. Liyun Zuo
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  2. Guangzhi Du
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Correspondence to Liyun Zuo.

Additional information

Communicated by A. Quarteroni

Subsidized by the National Nature Science Foundation of China (Grant Nos. 11701343, 11571274, 11401466) and the Provincial Natural Science Foundation of Shandong (Grant No. ZR2017BA027).

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Zuo, L., Du, G. A Multi-grid Decoupling Method for the Coupled Fluid Flow with the Porous Media Flow. J. Math. Fluid Mech. 20, 683–695 (2018). https://doi.org/10.1007/s00021-017-0340-7

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  • DOI: https://doi.org/10.1007/s00021-017-0340-7

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