  This paper introduces a sharp interface method to simulate fluid-structure
interaction (FSI) involving rigid bodies immersed in viscous incompressible
fluids. The capabilities of this methodology are demonstrated for a range of
benchmark test cases along with large-scale models of biomedical FSI. The
numerical approach developed herein, which we refer to as an immersed
Lagrangian-Eulerian method, integrates aspects of partitioned and immersed FSI
formulations by solving separate momentum equations for the fluid and solid
subdomains, as in a partitioned formulation, while also using non-conforming
discretizations of the dynamic fluid and structure regions, as in an immersed
formulation. A Dirichlet-Neumann coupling scheme is used, in which the motion
of the immersed solid is driven by fluid traction forces evaluated along the
fluid-structure interface, and the motion of the fluid along that interface is
constrained to match the solid velocity and thereby satisfy the no-slip
condition. To develop a practical numerical method, we adopt a penalty approach
that approximately imposes the no-slip condition along the fluid-structure
interface. Our fluid-structure interaction scheme relies on an immersed
interface method for discrete geometries, which enables the accurate
determination of both velocities and stresses along complex fluid-structure
interfaces. Unlike commonly used partitioned FSI methods, which can suffer from
so-called added mass effect instabilities, our methodology retains stability
for test cases involving extremely small, nearly equal, equal, and large
solid-fluid density ratios without requiring subiterations or complex handling
of the pressure. Biomedical FSI demonstration cases are also presented
including the dynamics of a bileaflet mechanical heart valve in a pulse
duplicator, and transport of blood clots in a patient-averaged anatomical model
of the inferior vena cava.
