Pressure data-driven variational multiscale reduced order models

In this paper, we develop data-driven closure/correction terms to increase the pressure and velocity accuracy of reduced order models (ROMs) for fluid flows. Specifically, we propose the first pressure-based data-driven variational multiscale ROM, in which we use the available data to construct closure/correction terms for both the momentum equation and the continuity equation. Our numerical investigation of the two-dimensional flow past a circular cylinder at Re = 50,000 in the marginally-resolved regime shows that the novel pressure data-driven variational multiscale ROM yields significantly more accurate velocity and pressure approximations than the standard ROM and, more importantly, than the original data-driven variational multiscale ROM (i.e., without pressure components). In particular, our numerical results show that adding the closure/correction term in the momentum equation significantly improves both the velocity and the pressure approximations, whereas adding the closure/correction term in the continuity equation improves only the pressure approximation. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this paper, data-driven closure/correction terms are developed to improve the accuracy of pressure and velocity in reduced order models (ROMs) for fluid flows. The proposed pressure-based data-driven variational multiscale ROM uses available data to construct closure/correction terms for the momentum equation and continuity equation. Numerical investigation shows that the novel pressure data-driven variational multiscale ROM yields significantly more accurate velocity and pressure approximations compared to the standard ROM and the original data-driven variational multiscale ROM without pressure components.