We propose a new data-driven reduced order model (ROM) framework that centers around
the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data …

For over a century, reduced order models (ROMs) have been a fundamental discipline of
theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr …

Abstract Galerkin and Petrov–Galerkin projection-based reduced-order models (ROMs) of
transient partial differential equations are typically obtained by performing a dimension …

Galerkin reduced order models (ROMs), eg, based on proper orthogonal decomposition
(POD) or reduced basis methods, have achieved significant success in the numerical …

In this paper, we present a brief tutorial on reduced order model (ROM) closures. First, we
carefully motivate the need for ROM closure modeling in under-resolved simulations. Then …

In this paper, we propose, analyze and test a post-processing implementation of a projection-
based variational multiscale (VMS) method with proper orthogonal decomposition (POD) for …

In this paper, we investigate the modeling of sub-scale components of proper orthogonal
decomposition reduced order models (POD-ROMs) of convection-dominated flows. We …

We extend the post-processing implementation of a projection based variational multiscale
(VMS) method with proper orthogonal decomposition (POD) to flows governed by double …

This paper studies a reduced-order model based on proper orthogonal decomposition
(POD) for the incompressible Navier-Stokes equations. The difficulties resulting from …

This paper considers the incompressible Navier-Stokes equations (NSE) in the
dimensionless form: 𝒖𝑡− 𝜈 Δ 𝒖+(𝒖⋅∇) 𝒖+∇ 𝑝= 𝒇 𝑖𝑛 (0, 𝜏]× Ω,∇⋅ 𝒖= 0 𝑖𝑛 (0, 𝜏]× Ω, 𝒖 …