A stable loosely coupled Fluid Structure Interaction scheme using sharp interface immersed boundary method for low to moderate mass ratios

Abstract

The stability of fluid–structure interaction (FSI) problems using immersed boundary (IB) method is an active area of research. In this regime, strong coupling is generally used to ensure stability and robustness. Strong coupling, however, is computationally expensive owing to its iterative nature. In the present work, we showcase the application of loose coupling algorithm for FSI problems using the sharp interface IB method specifically for low to moderate mass ratios (defined as the ratio of the mass of the structure to the mass of the fluid at the same volume). We demonstrate several test cases: vortex-induced vibration (VIV) of a cylinder, the effect of hinged leaflets attached to the exit of a piston in a channel, sedimentation of a circular disk, and bi-leaflet mechanical heart valves (BMHV) made of lightweight materials in physiological flow. We found our loose coupling method to be stable in all the test cases and obtained a linear relationship between the grid resolution employed and the lowest mass ratio for stable computations in the case of VIV of cylinder. Thus, a significant finding of our work is that with a reduction in grid spacing, one can achieve stable FSI simulation involving lower mass ratios using loosly-coupled schemes. We have deployed the present technique to investigate the dynamics of very low-density cylinders and hinged leaflets due to the fluid forces on them. The current method is extended to handle flexible bodies, such as vortex-induced vibrations of an elastic plate attached to a rigid cylinder and stable simulations are obtained when the Young’s modulus of the elastic plate is varied.