Physically-Constrained Data-Driven, Filtered Reduced Order Modeling of Fluid Flows

TL;DR

This paper introduces a physically-constrained data-driven filtered reduced order model (CDDF-ROM) for fluid flows, enhancing physical accuracy by enforcing conservation laws, and demonstrates its improved performance over previous models in simulating 2D flow past a cylinder.

Contribution

The paper develops a physically-constrained version of the DDF-ROM by incorporating physical laws into the data-driven modeling process, improving accuracy in fluid flow simulations.

Findings

CDDF-ROM outperforms DDF-ROM in accuracy.

Physical constraints improve model reliability.

Effective in both reproductive and predictive regimes.

Abstract

In our earlier work, we proposed a data-driven filtered reduced order model (DDF-ROM) framework for the numerical simulation of fluid flows, which can be formally written as \begin{equation*} \boxed{ \text{ DDF-ROM = Galerkin-ROM + Correction } } \end{equation*} The new DDF-ROM was constructed by using ROM spatial filtering and data-driven ROM closure modeling (for the Correction term) and was successfully tested in the numerical simulation of a 2D channel flow past a circular cylinder at Reynolds numbers $Re=100, Re=500$ and $Re=1000$. In this paper, we propose a {\it physically-constrained} DDF-ROM (CDDF-ROM), which aims at improving the physical accuracy of the DDF-ROM. The new physical constraints require that the CDDF-ROM operators satisfy the same type of physical laws (i.e., the nonlinear operator should conserve energy and the ROM closure term should be dissipative) as those satisfied by the fluid flow equations. To implement these physical constraints, in the data-driven modeling step of the DDF-ROM, we replace the unconstrained least squares problem with a constrained least squares problem. We perform a numerical investigation of the new CDDF-ROM and standard DDF-ROM for a 2D channel flow past a circular cylinder at Reynolds numbers $Re=100, Re=500$ and $Re=1000$. To this end, we consider a reproductive regime as well as a predictive (i.e., cross-validation) regime in which we use as little as $50\%$ of the original training data. The numerical investigation clearly shows that the new CDDF-ROM is significantly more accurate than the DDF-ROM in both regimes.