A Pressure-Stabilized Continuous Data Assimilation Reduced Order Model

TL;DR

This paper introduces a pressure-stabilized reduced-order model for 2D Navier-Stokes equations using continuous data assimilation, improving stability and efficiency by incorporating pressure modes and bypassing the inf-sup condition.

Contribution

It proposes a novel pressure stabilization strategy within a POD-ROM framework using CDA, enabling stable, accurate, and efficient reduced-order solutions without the inf-sup condition.

Findings

Unconditional stability and convergence of the proposed ROM.

Validation through benchmark tests confirming theoretical results.

Enhanced computational efficiency due to decoupling of velocity and pressure.

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.