A sharp interface Lagrangian-Eulerian method for rigid-body fluid-structure interaction

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.