Principal interval decomposition framework for POD reduced-order modeling of convective Boussinesq flows

A principal interval decomposition (PID) approach is presented for the reduced-order modeling of unsteady Boussinesq equations. The PID method optimizes the lengths of the time windows over which proper orthogonal decomposition (POD) is performed and can be highly effective in building reduced-order models for convective problems. The performance of these POD models with and without using the PID approach is investigated by applying these methods to the unsteady lock-exchange flow problem. This benchmark problem exhibits a strong shear flow induced by a temperature jump and results in the Kelvin-Helmholtz instability. This problem is considered a challenging benchmark problem for the development of reduced-order models. The reference solutions are obtained by direct numerical simulations of the vorticity and temperature transport equations using a compact fourth-order-accurate scheme. We compare the accuracy of reduced-order models developed with different numbers of POD basis functions and different numbers of principal intervals. A linear interpolation model is constructed to obtain basis functions when varying physical parameters. The predictive performance of our models is then analyzed over a wide range of Reynolds numbers. It is shown that the PID approach provides a significant improvement in accuracy over the standard Galerkin POD reduced-order model. This numerical assessment of the PID shows that it may represent a reliable model reduction tool for convection-dominated, unsteady-flow problems. Copyright (c) 2015 John Wiley & Sons, Ltd.