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arXiv · 2201.07398

An efficient Chorin-Temam projection proper orthogonal decomposition based reduced-order model for nonstationary Stokes equations

Xi Li·Yan Luo·Minfu Feng
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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 POD 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 first obtain the convergence of PSPG-type finite element projection scheme, and then analyze the proposed projection POD-ROM's stability and convergence. Numerical experiments validate out theoretical results.

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Xi Li, Yan Luo, Minfu Feng. 2022-01-19. An efficient Chorin-Temam projection proper orthogonal decomposition based reduced-order model for nonstationary Stokes equations. https://doi.org/10.1007/s10915-022-02032-1

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