Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations

TL;DR

This paper develops a stabilized reduced order modeling approach for the incompressible Navier-Stokes equations using finite volume discretization and POD, comparing two pressure stabilization strategies for improved accuracy at moderate Reynolds numbers.

Contribution

It introduces a stabilized POD-Galerkin reduced order method with two novel pressure stabilization techniques for finite volume discretized Navier-Stokes equations.

Findings

The proposed methods effectively stabilize the reduced order model.

Comparison shows differences in stabilization effectiveness between the two strategies.

The approach is suitable for moderate Reynolds number flows.

Abstract

In this work a stabilised and reduced Galerkin projection of the incompressible unsteady Navier-Stokes equations for moderate Reynolds number is presented. The full-order model, on which the Galerkin projection is applied, is based on a finite volumes approximation. The reduced basis spaces are constructed with a POD approach. Two different pressure stabilisation strategies are proposed and compared: the former one is based on the supremizer enrichment of the velocity space, and the latter one is based on a pressure Poisson equation approach.