A monolithic mathematical framework for understanding the fluid-rigid-elastic structure interaction problem is proposed. A numerical method in a secondary formulation of the Navier-Stokes equations accompanying a technique for imposing the rigid boundaries is applied. The one-fluid formulation of the incompressible Navier-stokes equation, containing the terms governing the elastic structure, is transformed into the vorticity-stream function formulation. The rigid structure is imposed in the flow field based on the velocity-vorticity kinematic relation and harmonic function theorem. The vorticity, level-set function, and left Cauchy-Green deformation tensor are updated utilizing three transport equations to investigate the evolution of the velocity field, elastic structure(s) configuration, and elastic stress tensor. The method is implemented to solve three challenging problems, and the results show its capabilities in proper imposing the rigid structures in the flow field and also the simultaneous modeling the rigid and elastic structure interactions with incompressible fluid flow.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.