A Pressure-Stabilized Continuous Data Assimilation Reduced Order Model for Incompressible Navier-Stokes Equations

We present a novel reduced-order pressure stabilization strategy based on continuous data assimilation (CDA) technique for the two-dimensional incompressible Navier-Stokes equations. A feedback control term is incorporated into the pressure-correction projection method to derive a Galerkin projection-based CDA proper orthogonal decomposition reduced order model. This model simultaneously utilizes pressure modes and velocity modes to compute stable and accurate reduced-order solutions. The significant advantage of this ROM is that, with the help of CDA, the standard discrete inf-sup condition is circumvented for the mixed POD velocity-pressure spaces, resulting in a priori stable and highly accurate reduced-order simulations. Furthermore, the classical projection method decouples reduced-order velocity and pressure fields, thereby further enhancing computational efficiency. We present stability and convergence analyses over POD modes (up to discretization error), and validate the theoretical results through several numerical experiments.