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In the present work, we propose a novel immersed boundary method for the study of strongly coupled fluid-structure interaction problem. In the immersed boundary formulation, the interaction of the fluid and the structure is realized through a boundary force. This force is added to the fluid momentum equation as a source term, hence the fluid equations are solved on a fixed Eulerian grid regardless the movement of solid. This greatly accelerates the computation and circumvents the dynamic mesh issues encountered by the traditional body-conforming mesh methods (e.g. arbitrary Lagrangian–Eulerian method). 

The novel method consists of an implicit algorithm for imposing the no-slip wall condition at the immersed fluid-structure interface and an efficient iterative scheme for updating the fluid and solid variables simultaneously at each time step. The boundary force employed in the novel immersed boundary method is determined implicitly with an additional force equation. The coefficient matrix of the force equation is formulated to be symmetric and positive-definite, so that the conjugate gradient method can solve it very quickly. The present method is tested with numerical examples and compared to the well established benchmark. The following figures show the motion of a freely falling elliptical particle in a confined channel.

numerical methods