Streamline penetration, velocity error, and consequences of the feedback immersed boundary method

This paper presents a study on streamline penetration, velocity error, and consequences of a fluid-structure interaction (FSI) solver based on the feedback immersed boundary method (IBM). In the FSI solver, the fluid dynamics is solved by the lattice Boltzmann method; the solid structure deformation is solved by the finite difference method and the finite element method for two- and three-dimensional cases, respectively; and the feedback IBM is used to realize the interaction between the fluid and the structure. The IBM is implemented in non-iterative and iterative ways. For the non-iterative version, two types of integration are discussed: without and with velocity prediction step. Five benchmark cases are simulated to study the performance of the three implementations: a uniform flow over a cylinder, flow-induced vibration of a flexible plate attached behind a stationary cylinder in a channel, flow through a two-dimensional asymmetric stenosis, a one-sided collapsible channel, and a three-dimensional collapsible tube. Results show that both the IBM with prediction step, the iterative IBM, and one iteration IBM with proper feedback coefficients can suppress the spurious flow penetration on the solid wall. While the velocity error does not significantly affect the force production and structure deformation for external flows, reducing it significantly improves the prediction of the force distribution and structure deformation for internal flows. In addition, the iterative IBM with smaller feedback coefficient has better numerical stability. This work will provide an important guideline for the correct use of the feedback IBMs.