Using a proper orthogonal decomposition to elucidate features in granular flows

Proper Orthogonal Decomposition Closure Models for Fluid Flows: Burgers Equation

This paper puts forth several closure models for the proper orthogonal decomposition (POD) reduced order modeling of fluid flows. These new closure models, together with other standard closure models, are investigated in the numerical simulation of the Burgers equation. This simplified setting represents just the first step in the investigation of the new closure models. It allows a thorough as...

Proper Orthogonal Decomposition Technique for Transonic Unsteady Aerodynamic Flows

A new method for constructing reduced-order models (ROM) of unsteady small-disturbance  ows is presented. The reduced-order models are constructed using basis vectors determined from the proper orthogonal decomposition (POD) of an ensemble of small-disturbance frequency-domain solutions. Each of the individual frequencydomain solutions is computed using an efŽ cient time-linearized  ow solver...

An introduction to the proper orthogonal decomposition

A tutorial is presented on the Proper Orthogonal Decomposition (POD), which finds applications in computationally processing large amounts of high-dimensional data with the aim of obtaining low-dimensional descriptions that capture much of the phenomena of interest. The discrete version of the POD, which is the singular value decomposition (SVD) of matrices, is described in some detail. The con...

Artificial viscosity proper orthogonal decomposition

We introduce improved reduced-order models for turbulent flows. These models are inspired from successful methodologies used in large eddy simulation, such as artificial viscosity, applied to standardmodels created by proper orthogonal decomposition of flows coupled with Galerkin projection. As a first step in the analysis and testing of our new methodology, we use the Burgers equation with a s...

Low Dimensional Azimuthal Characteristics of Suddenly Expanding Axisymmetric Flows using Proper Orthogonal and Fourier Decomposition