论文标题
一个有效的基于基于非组织stokes方程的基于正交分解模型的高效脉络蛋白-TEMAM投影
An efficient Chorin-Temam projection proper orthogonal decomposition based reduced-order model for nonstationary Stokes equations
论文作者
论文摘要
在本文中，我们提出了一种有效的适当的基于正交分解的降低阶模型（POD-ROM），用于非组织的Stokes方程，该方程将经典投影方法与POD技术相结合。该新方案主要拥有两个优点：第一个方案是低计算成本，因为经典投影方法将降低的速度变量和降级压力变量变量分解，并且POD技术进一步提高了计算效率；第二个优势包括绕过借助压力稳定的Petrov-Galerkin（PSPG） - 型投影方法对混合POD空间进行经典LBB/INF-SUP条件的验证，其中压力稳定项是固有的，允许使用不增加额外稳定术语的非Inff-Sup稳定元素。我们首先获得PSPG型有限元投影方案的收敛性，然后分析提出的投影POD-ROM的稳定性和收敛性。数值实验验证了理论结果。
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.
