An Adaptive Time Filtered Backward Euler Method for Reduced-Order Models of Incompressible Flows

Abstract

This paper studies a reduced-order model based on proper orthogonal decomposition (POD) for the incompressible Navier-Stokes equations. The difficulties resulting from nonlinearity are eliminated using the variational multiscale (VMS) method. The time filter is added as a separate post-processing step to the standard VMS-POD approximation. This increases the accuracy and presents a better energy preserving scheme without adding additional computational complexity. Theoretical analyses of the method are given. Numerical experiments are presented to verify the theoretical findings.