A full-Eulerian approach for simulation of a system of fluid–rigid–elastic structure interaction based on the vorticity-stream function formulation

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.