Immersed boundary methods for fluid-structure interaction: A review

In this review, we introduce immersed boundary (IB) methods for fluid-structure interactions (FSIs) of rigid and elastic bodies. IB methods impose momentum forcing on an Eulerian mesh to satisfy boundary conditions on the interface between fluid and structure, which enables us to use a non-body conforming grid system for complex-shaped moving bodies. Imposition of the momentum forcing is performed directly through discrete delta function or indirectly through velocity reconstruction, by which IB methods have their own strengths and weaknesses to FSI problems of rigid and elastic bodies. To deal with FSI, IB methods using monolithic and partitioned (strong and weak coupling) approaches with different stability and cost have been suggested. Nevertheless, two important problems in FSI, cases of low density ratio of solid to fluid and high Reynolds number, have not been completely overcome by current IB methods in terms of the stability, accuracy and cost. These aspects are examined in this review.