Time Adaptive POD Reduced Order Model for Viscous Incompressible Flows

A challenge in constructing proper orthogonal decomposition based reduced order model (POD-ROM) of nonlinear infinite dimensional system is its input dependency. In order to address this issue, we propose a time adaptive proper orthogonal decomposition reduced order model (POD-ROM) for the numerical simulation of viscous incompressible fluid flows. In particular, the new time adaptive POD-ROM is a velocity-pressure reduced order model that employs pressure basis functions as well to compute the reduced order pressure, needed to compute forces on bodies in the flow. We prove stability and error estimates for the reduced basis discretization of the adaptive POD-ROM under the assumption that the ratios of the adjacent time step sizes are bounded from above by a constant. We provide numerical comparison of the considered methods for a flow past airfoil problem.