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Two-Grid Arrow-Hurwicz Methods for the Steady Incompressible Navier-Stokes Equations

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Abstract

In this paper, three kinds of two-grid Arrow-Hurwicz (A-H) methods are proposed and analyzed for the steady incompressible Navier-Stokes equations, which adopt the existing A-H method to obtain the coarse mesh solution, and further enhance the efficiency by three different one-step schemes (Oseen type, Simple type and Newton type) on the fine mesh. These methods combine the A-H method and the two-grid strategy, retaining the best features of two techniques and overcoming some of their limitations. Furthermore, the error analyses of the three methods are carefully studied and the numerical tests are reported to demonstrate the theoretical results and show the efficiency of the methods.

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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors would like to thank two anonymous reviewers for valuable comments which helped to improve an early version of the paper.

Funding

The work of Prof. Jianguo Huang was partially supported by the National Key Research and Development Project (2020YFA0709800) and NSFC (Grant No. 12071289). The work of Prof. Haibiao Zheng was partially supported by NSFC (Grant No. 11971174), NSF of Shanghai (Grant No. 19ZR1414300) and Science and Technology Commission of Shanghai Municipality (Grant No. 18dz2271000).

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Authors and Affiliations

  1. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, China

    Binbin Du

  2. School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jianguo Huang

  3. School of Mathematical Sciences, East China Normal University, Shanghai, 200241, China

    Haibiao Zheng

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  1. Binbin Du
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  2. Jianguo Huang
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  3. Haibiao Zheng
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All authors contributed equally to this manuscript.

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Correspondence to Jianguo Huang.

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The authors have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this manuscript.

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The codes during the current study are available from the corresponding author on reasonable request.

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JH was partially supported by the National Key Research and Development Project (2020YFA0709800) and NSFC (Grant No. 12071289). HZ was partially supported by NSFC (Grant No. 11971174), NSF of Shanghai (Grant No. 19ZR1414300) and Science and Technology Commission of Shanghai Municipality (Grant No. 18dz2271000).

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Du, B., Huang, J. & Zheng, H. Two-Grid Arrow-Hurwicz Methods for the Steady Incompressible Navier-Stokes Equations. J Sci Comput 89, 24 (2021). https://doi.org/10.1007/s10915-021-01627-4

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  • DOI: https://doi.org/10.1007/s10915-021-01627-4

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