Proper orthogonal decomposition of by-pass transition data

Abstract

Reduced-order modeling of direct numerical simulations (DNS) data of by-pass transition over a zero pressure gradient shear layer is presented in the chapter in a proper orthogonal decomposition (POD) framework. Analysis of this complex unsteady vortex-dominated flow is done by locating the eigenvalues and eigenvectors of the covariance matrix by using Lanczos iteration. The local and global description produces eigenvectors that match seamlessly because of the linearity property of POD. The aim of this analysis tool is to identify long-term dynamical behavior of physical systems. Fluid flow at high Reynolds number displays very complicated spatio-temporal variation and is an ideal field where POD tools apply—as is shown in the chapter. POD has been used in engineering applications of fluid flows for unsteady aerodynamics, fluid-structure interaction, and turbomachine analysis that uses potential flow models. Although there are some viscous flow applications via boundary layer type of analysis, there are very few that actually use direct numerical simulation data.