The Flow-Induced Vibrations of Vocal Folds Approximated by the Finite Element Method

Abstract

This paper is interested in mathematical model and numerical simulation of the flow-induced vibrations of human vocal folds model. The elastic tissue of the vocal fold is described by the linear elasticity and the viscous fluid flow in the glottal channel is modelled with the aid of the incompressible Navier-Stokes equations. To incorporate the time change of the fluid domain into the flow description, the arbitrary Lagrangian-Eulerian (ALE) method is used. A special attention is paid to inlet boundary conditions. Besides the classical Dirichlet boundary condition the penalization approach is presented, which allows to relax the exact inlet velocity during the channel closing phase. Such a situation is highly interesting for simulation of human phonation. The developed numerical schemes for the fluid flow and the elastic body are implemented by an in-house solver based on the finite element method. Specially, the fluid flow scheme is approximated with the help of SUPG and PSPG stabilization methods. The implemented numerical partitioned scheme is strongly coupled. Finally, the numerical results of flow induced vibrations are presented and effects of the aforementioned inlet boundary conditions are discussed.