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. The stability and error analyses of the method are provided, and results of the several numerical tests are presented to verify the efficiency of the method in this setting.