非定常Stokes方程的一种基于Chorin-Temam投影的本征正交分解降阶模型
An efficient Chorin-Temam projection proper orthogonal decomposition based reduced-order model for nonstationary Stokes equations
AI总结：
针对非定常Stokes方程，提出结合经典投影与POD技术的降阶模型，通过解耦变量降低计算成本，并利用PSPG型投影规避LBB条件，理论分析与数值实验均验证了其稳定性和收敛性。
摘要：
本文针对非stationary Stokes方程，提出了一种结合经典投影方法与POD技术的高效基于本征正交分解的降阶模型(POD-ROM)。该新方案主要有两大优势：首先是低计算成本，因为经典投影方法解耦了降阶速度变量与降阶压力变量，且POD技术进一步提升了计算效率；其次，借助压力稳定化Petrov-Galerkin(PSPG)型投影方法，规避了对混合POD空间经典LBB/inf-sup条件的验证，其中压力稳定项是固有的，允许在不添加额外稳定项的情况下使用非inf-sup稳定单元。我们首先获得了PSPG型有限元投影方案的收敛性，随后分析了所提投影POD-ROM的稳定性和收敛性。数值实验验证了我们的理论结果。
英文摘要：
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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