A Pressure-Stabilized Continuous Data Assimilation Reduced Order Model

2023/04/01 by Xi Li, Li, Xi, Youcai Xu +3 · 1 citation
Physics and Astronomy · Engineering · #Model Reduction and Neural Networks #Computational Fluid Dynamics and Aerodynamics #Fluid Dynamics and Vibration Analysis

paper · pdf · doi:10.48550/arxiv.2304.00289

Abstract

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.

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