A moving-least-squares immersed boundary method for simulating the fluid–structure interaction of elastic bodies with arbitrary thickness

A versatile numerical method is presented to predict the fluid–structure interaction of bodies with arbitrary thickness immersed in an incompressible fluid, with the aim of simulating different biological engineering applications. A direct-forcing immersed boundary method is adopted, based on a moving-least-squares approach to reconstruct the solution in the vicinity of the immersed surface. A simple spring-network model is considered for describing the dynamics of deformable structures, so as to easily model and simulate different biological systems that not always may be described by simple continuum models, without affecting the computational time and simplicity of the overall method. The fluid and structures are coupled in a strong way, in order to avoid instabilities related to large accelerations of the bodies. The effectiveness of the method is validated by means of several test cases involving: rigid bodies, either falling in a quiescent fluid, fluttering or tumbling, or transported by a shear flow; infinitely thin elastic structures with mass, such as a two-dimensional flexible filament and, concerning three-dimensional cases, a flapping flag and an inverted flag in a free stream; finally, a three-dimensional model of a bio-prosthetic aortic valve opening and closing under a pulsatile flowrate. A very good agreement is obtained in all the cases, comparing with available experimental data and numerical results obtained by different methods. In particular, the method is shown to be second-order accurate by means of a mesh-refinement study. Moreover, it is able to provide results comparable with those of sharp direct-forcing approaches, and can manage high pressure differences across the surface, still obtaining very smooth hydrodynamic forces.