A POD-Galerkin reduced order model for the Navier-Stokes equations in stream function-vorticity formulation

TL;DR

This paper introduces a novel POD-Galerkin reduced order model for the Navier-Stokes equations in stream function-vorticity form, using separate coefficients and a global basis for efficient parametric simulations.

Contribution

It proposes a new ROM approach with distinct coefficients for vorticity and stream function, and employs a global POD basis for parametric studies, improving efficiency and accuracy.

Findings

Effective in vortex merger benchmark

Accurate time reconstruction and parametric analysis

Enhanced computational efficiency

Abstract

We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier-Stokes equations in the stream function-vorticity formulation. Unlike previous works, we choose different reduced coefficients for the vorticity and stream function fields. In addition, for parametric studies we use a global POD basis space obtained from a database of time dependent full order snapshots related to sample points in the parameter space. We test the performance of our ROM strategy with the vortex merger benchmark. Accuracy and efficiency are assessed for both time reconstruction and physical parametrization.