Simulation of the interaction between flexible structure and ambient fluid flow by the immersed boundary method

Abstract

An improved version of the immersed boundary method is developed for simulating the interaction between flexible structure and ambient fluid flow. The proposed method is based on an efficient Navier-Stokes solver adopting the fractional step method and a staggered Cartesian grid system. In the present method, the fluid motion is defined on an Eulerian grid, while the structure motion is defined on a Lagrangian grid, and they are solved independently. The fluid-structure interaction is formulated through an additional momentum forcing which is calculated explicitly using the feedback law or the structure motion equation. The method is first applied to a flow over a flexible inextensible filament. The mechanism by which small vortex processions are produced is investigated, and the bistable property of the system is observed by altering the filament length. For two side-by-side filaments in a uniform flow, both in-phase flapping and out-of-phase flapping are reproduced in the present study. Then we extend the method to three-dimensional simulation of a flapping flag in a uniform flow. The instantaneous flag motion was analyzed under different conditions and the surrounding vortical structures were visualized. The Strouhal number defined in terms of the flapping amplitude is located in the range 0.16~0.22, consistent with the values reported for flying or swimming animals. The onset of regular flapping was found to be subcritical in our simulation. Toward applications in biofluid problems, we modeled fluid motion around two-dimensional deformable bodies with thickness, which are discretized in a non-uniform Lagrangian mesh and interact with surrounding fluid only along the interface. Three examples are presented: a cavity flow with a deformable volume at the bottom, a swimming jellyfish, and a deformable circular ring moving through a channel with contraction.