# Pod-Galerkin Reduced Order Methods for CFD Using Finite Volume Discretisation: Vortex Shedding Around a Circular Cylinder

## TL;DR

This paper develops a POD-Galerkin reduced order model for simulating vortex shedding around a circular cylinder using finite volume discretization, focusing on accurate pressure field reproduction and adapting standard methods to finite volume frameworks.

## Contribution

It introduces a finite volume POD-Galerkin ROM for CFD, emphasizing pressure accuracy and separate basis spaces for velocity and pressure.

## Key findings

- ROM accurately reproduces vortex shedding phenomena
- Effective pressure field modeling for drag and lift calculations
- Adaptation of POD-Galerkin methods to finite volume discretization

## Abstract

Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible flow around a circular cylinder is presented in this work. The ROM is built performing a Galerkin projection of the governing equations onto a lower dimensional space. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) the projection of the Governing equations (momentum equation and Poisson equation for pressure) performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework. The accuracy of the reduced order model is assessed against full order results.