Hybrid Data-Driven Closure Strategies for Reduced Order Modeling

TL;DR

This paper introduces hybrid data-driven closure strategies for reduced order models of fluid flows, combining purely data-driven corrections with physically based eddy viscosity modeling, leading to improved accuracy.

Contribution

It presents the first combination of two different ROM closure strategies, enhancing model accuracy for complex fluid flow simulations.

Findings

Hybrid ROMs outperform purely data-driven models.

Hybrid approach improves accuracy in flow past a cylinder.

Machine learning effectively determines eddy viscosity terms.

Abstract

In this paper, we propose hybrid data-driven ROM closures for fluid flows. These new ROM closures combine two fundamentally different strategies: (i) purely data-driven ROM closures, both for the velocity and the pressure; and (ii) physically based, eddy viscosity data-driven closures, which model the energy transfer in the system. The first strategy consists in the addition of closure/correction terms to the governing equations, which are built from the available data. The second strategy includes turbulence modeling by adding eddy viscosity terms, which are determined by using machine learning techniques. The two strategies are combined for the first time in this paper to investigate a two-dimensional flow past a circular cylinder at Re=50000. Our numerical results show that the hybrid data-driven ROM is more accurate than both the purely data-driven ROM and the eddy viscosity ROM.