论文标题
用于基于POD的准地神经方程的基于POD的降序模型的线性滤波器正则化
A linear filter regularization for POD-based reduced order models of the quasi-geostrophic equations
论文作者
论文摘要
我们提出了一个准斑块方程（QGE）的降低订单模型（ROM）的正则化，以提高准确性，而当保留的适当的正交分解（POD）模式保留以构建减少基础的基础不足以描述系统动力学。我们的正则化基于所谓的BV-Alpha模型，该模型修改了QGE中的非线性项，并为涡度添加了线性微分滤波器。为了显示BV-Alpha模型在ROM闭合中的有效性，我们比较了由Pod-Galerkin ROM计算出的结果，该结果具有经典的双gyre风力强迫基准，并没有正则化。我们的数值结果表明，即使保留的POD模式占特征值的一小部分，由正则化ROM计算的解决方案也更准确。此外，我们表明，尽管计算上的昂贵比没有正规化的ROM更昂贵，但正则化ROM仍然是QGE全订单模拟的竞争替代方案。
We propose a regularization for Reduced Order Models (ROMs) of the quasi-geostrophic equations (QGE) to increase accuracy when the Proper Orthogonal Decomposition (POD) modes retained to construct the reduced basis are insufficient to describe the system dynamics. Our regularization is based on the so-called BV-alpha model, which modifies the nonlinear term in the QGE and adds a linear differential filter for the vorticity. To show the effectiveness of the BV-alpha model for ROM closure, we compare the results computed by a POD-Galerkin ROM with and without regularization for the classical double-gyre wind forcing benchmark. Our numerical results show that the solution computed by the regularized ROM is more accurate, even when the retained POD modes account for a small percentage of the eigenvalue energy. Additionally, we show that, although computationally more expensive that the ROM with no regularization, the regularized ROM is still a competitive alternative to full order simulations of the QGE.
