A Spectral Vanishing Viscosity Method for Stabilizing Low-Dimensional Galerkin Systems

Abstract

Low-dimensional flow dynamical systems are susceptible to instabilities after longtime integration. In this paper, we investigate the stability 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, instabilities arise after a few hundred vortex shedding cycles. We then propose a dissipative model based on a spectral vanishing viscosity (SVV) diffusion convolution operator as an effective way of stabilizing low-dimensional Galerkin systems.