# An Artificial Compression Reduced Order Model

## TL;DR

The paper introduces a novel artificial compression reduced order model (AC-ROM) for simulating viscous incompressible flows, providing accurate velocity and pressure approximations without strict mathematical constraints on the basis functions.

## Contribution

It presents a new AC-ROM that relaxes traditional stability conditions and constructs basis functions from non-divergence-free data, with proven error estimates and numerical validation.

## Key findings

- AC-ROM accurately approximates velocity and pressure.
- The model does not require inf-sup condition for basis functions.
- Numerical experiments confirm the effectiveness of AC-ROM.

## Abstract

We propose a novel artificial compression, reduced order model (AC-ROM) for the numerical simulation of viscous incompressible fluid flows. The new AC-ROM provides approximations not only for velocity, but also for pressure, which is needed to calculate forces on bodies in the flow and to connect the simulation parameters with pressure data. The new AC-ROM does not require that the velocity-pressure ROM spaces satisfy the inf-sup (Ladyzhenskaya-Babuska-Brezzi) condition and its basis functions are constructed from data that are not required to be weakly-divergence free. We prove error estimates for the reduced basis discretization of the AC-ROM. We also investigate numerically the new AC-ROM in the simulation of a two-dimensional flow between offset cylinders.