Coupling the Curvilinear Immersed Boundary Method with Rotation-Free Finite Elements for Simulating Fluid–Structure Interaction: Concepts and Applications

The sharp interface curvilinear immersed boundary (CURVIB) method coupled with a rotation-free finite element (FE) method for thin shells provides a powerful framework for simulating fluid–structure interaction (FSI) problems for geometrically complex, arbitrarily deformable structures. The CURVIB and FE solvers are coupled together on the flexible solid–fluid interfaces, which contain the structural nodal positions, displacements, velocities, and loads calculated at each time level and exchanged between the flow and structural solvers. Loose and strong coupling FSI schemes are employed, enhanced by the Aitken acceleration technique to ensure robust coupling and fast convergence, especially for low mass ratio problems. Large-eddy simulation (LES) of turbulent flow FSI problems employ the dynamic Smagorinsky subgrid scale model with a wall model for reconstructing velocity boundary conditions near the immersed boundaries. In this chapter, the CURVIB-FE FSI algorithm is reviewed and its capabilities are demonstrated via a series of examples involving thin flexible structures undergoing very large deformations. The inverted flag problem is employed to validate the method, and the problem of a tri-leaflet aortic valve in an anatomic aorta is employed to demonstrate its potential in complex cardiovascular flow applications.