Fluid-Structure Interaction (FSI) algorithm
Fluid-structure interactions (FSI) are involved in many engineering and bio-mechanical systems. The Immersed Finite Element Method (IFEM) is a numerical tool to solve FSI problems that utilizes fully-coupled fluid and solid using non-conforming meshes. It allows large deformation or movement of the solid without mesh update or re-meshing.
Acoustic wave propagation is particularly important in studying sound production where the acoustic wave is induced by fluid-structure interactions. To compute the generation and propagation of the waves, we modify the continuity equation by instituting the isentropic relationship between the variation of pressure and density such that slight compressibility is ensured (for low Mach number flows). The slightly compressible fluid is then fully coupled with a nonlinear solid solver using the Immersed Finite Element Method (IFEM) technique to compute sound generation, propagation, and frequency modes in acoustic-fluid-structure interaction problems. By applying appropriate acoustic boundaries such as resonators and absorbing boundaries, accurate acoustic behaviors as well as tissue deformations are captured.