We present a novel reduced-order pressure stabilization strategy based on continuous data assimilation(CDA) for two-dimensional incompressible Navier-Stokes equations. A feedback control term is incorporated into pressure-correction projection method to derive the Galerkin projection-based CDA proper orthogonal decomposition reduced order model(POD-ROM) that uses pressure modes as well as velocity's simultaneously to compute the reduced-order solutions. The greatest advantage over this ROM is circumventing the standard discrete inf-sup condition for the mixed POD velocity-pressure spaces with the help of CDA which also guarantees the high accuracy of reduced-order solutions; moreover, the classical projection method decouples reduced-order velocity and pressure, which further enhances computational efficiency. Unconditional stability and convergence over POD modes(up to discretization error) are presented, and a benchmark test is performed to validate the theoretical results.

翻译：我们提出了一种新颖的基于连续数据同化(CDA)的压力稳定化降阶策略，适用于二维不可压缩Navier-Stokes方程。通过在压力修正投影法中引入反馈控制项，推导出基于Galerkin投影的CDA本征正交分解降阶模型(POD-ROM)，该模型同时利用压力模态与速度模态计算降阶解。该降阶模型的最大优势在于：借助CDA规避了混合POD速度-压力空间的标准离散inf-sup条件，同时保证了降阶解的高精度；此外，经典投影法对降阶速度与压力进行解耦，进一步提升了计算效率。本文给出了关于POD模态的无条件稳定性与收敛性分析（误差可达离散误差量级），并通过基准测试验证了理论结果。