Stabilized POD Reduced Order Models for convection-dominated incompressible flows

TL;DR

This paper compares two stabilization techniques for POD reduced order models to improve simulation accuracy of convection-dominated incompressible flows, demonstrating significant improvements over non-stabilized models.

Contribution

It introduces and evaluates two novel stabilization methods for POD-Galerkin ROMs applied to convection-dominated flows, enhancing their accuracy and efficiency.

Findings

Both stabilization methods significantly improve ROM accuracy.

Adding mode-dependent artificial viscosity yields better results than a global viscosity.

The stabilized ROMs perform well in a medical device flow simulation.

Abstract

We present a comparative computational study of two stabilized Reduced Order Models (ROMs) for the simulation of convection-dominated incompressible flow (Reynolds number of the order of a few thousands). Representative solutions in the parameter space, which includes either time only or time and Reynolds number, are computed with a Finite Volume method and used to generate a reduced basis via Proper Orthogonal Decomposition (POD). Galerkin projection of the Navier-Stokes equations onto the reduced space is used to compute the ROM solution. To ensure computational efficiency, the number of POD modes is truncated and ROM solution accuracy is recovered through two stabilization methods: i) adding a global constant artificial viscosity to the reduced dimensional model, and ii) adding a different value of artificial viscosity for the different POD modes. We test the stabilized ROMs for fluid flow in an idealized medical device consisting of a conical convergent, a narrow throat, and a sudden expansion. Both stabilization methods significantly improve the ROM solution accuracy over a standard (non-stabilized) POD-Galerkin model.