Sharp interface immersed boundary methods and their application to vortex-induced vibration of a cylinder

The sharp interface immersed boundary method is assessed for suitability and accuracy in simulating flow-induced vibration, specifically the phenomenon of vortex-induced vibration (VIV) in the two-dimensional flow past an elastically-mounted cylinder. Inherent to immersed boundary methods are the spurious force oscillations observed when the immersed boundary moves across the underlying grid. This deficiency in immersed boundary methods is acute in flows featuring fully-coupled fluid-structure interaction, where these oscillations are fed directly back into the coupled system and have the potential to significantly affect the solution. Here, the immersed boundary method is tested and compared directly and in detail to an accurate and validated spectral-element method. The immersed boundary method performs well for the given problem, excepting a few cases, such as those featuring disordered vortex-shedding. A heuristic model is developed to analyze the frequency content of the observed spurious force oscillations and their potential to affect the global solution. A guide to the resolution required for spatial accuracy is proposed, that around 40 points should span the peak-to-peak distance of any significant oscillation.