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An Efficient Chorin–Temam Projection Proper Orthogonal Decomposition Based Reduced-Order Model for Nonstationary Stokes Equations

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Abstract

In this paper, we propose an efficient proper orthogonal decomposition based reduced-order model (POD-ROM) for nonstationary Stokes equations, which combines the classical projection method with POD technique. This new scheme mainly owns two advantages: the first one is low computational costs since the classical projection method decouples the reduced-order velocity variable and reduced-order pressure variable, and POD technique further improves the computational efficiency; the second advantage consists of circumventing the verification of classical LBB/inf-sup condition for mixed reduced spaces with the help of pressure stabilized Petrov–Galerkin (PSPG)-type projection method, where the pressure stabilization term is inherent which allows the use of non inf-sup stable elements without adding extra stabilization terms. We analyze the proposed projection POD-ROM’s stability and convergence, and numerical experiments validate those theoretical results and also the high-efficiency.

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Acknowledgements

The authors thank the anonymous referees for their constructive comments and suggestions which improved the manuscript.

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  1. School of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, China

    Xi Li & Minfu Feng

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, China

    Yan Luo

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Xi Li and Minfu Feng: The work of this author was supported by the National Natural Science Foundation of China (Grant No. 11971337). Yan Luo: The work of this author was supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11901078) and by the Fundamental Research Funds for the Central Universities (Grant No. ZYGX2020J021).

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Li, X., Luo, Y. & Feng, M. An Efficient Chorin–Temam Projection Proper Orthogonal Decomposition Based Reduced-Order Model for Nonstationary Stokes Equations. J Sci Comput 93, 64 (2022). https://doi.org/10.1007/s10915-022-02032-1

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