A spectral viscosity method for correcting the long-term behavior of POD models

Low-dimensional flow dynamical systems may converge to erroneous states after long-time integration, even if they are initialized with the correct state. In this paper, we investigate the accuracy of such two-dimensional models constructed from Karhunen–Loeve expansions for flows past a circular cylinder. We first demonstrate that although the short-term dynamics may be predicted accurately with only a handful of modes retained, drifting of the solution may arise after a few hundred vortex shedding cycles. We then propose a dissipative model based on a spectral viscosity (SV) diffusion convolution operator. The parameters of the SV model are selected rigorously based on bifurcation analysis. Our results show that this is an effective way of improving the accuracy of long-term predictions of low-dimensional Galerkin systems.