Interval-Based Reduced-Order Models for Unsteady Fluid Flow

Abstract

A number of practical engineering problems require the repeated simulation of unsteady fluid flows. These problems include the control, optimization and uncertainty quantification of fluid systems. To make many of these problems tractable, reduced-order modeling has been used to minimize the simulation requirements. For nonlinear, time-dependent problems, such as the Navier-Stokes equations, reduced-order models are typically based on the proper orthogonal decomposition (POD) combined with Galerkin projection. We study several modifications to this reduced-order modeling approach motivated by the optimization problem underlying POD. Our discussion centers on a method known as the principal interval decomposition (PID) due to IJzerman.