Finite element approximation of flow induced vibrations of human vocal folds model: Effects of inflow boundary conditions and the length of subglottal and supraglottal channel on phonation onset

The paper presents the numerical analysis of interaction of the vibrating simplified human vocal folds model with the incompressible viscous airflow in a channel modeling simplified subglottal and supraglottal spaces. The flow in the considered 2D computational fluid domain is governed by the Navier-Stokes equations written in the Arbitrary Lagrangian-Eulerian form. The stabilized finite element method is applied for numerical approximation and the choice of boundary conditions and their implementation is discussed. For the considered model problem the prescribed inlet velocity and prescribed pressure difference formulations were numerically analyzed. The prescribed inlet velocity formulation was successful in predicting of the flutter velocity value, whereas the prescribed pressure difference gave nonphysical results. Finally a modified inlet boundary condition motivated by the penalization approach is suggested. It is shown that this approach gives possibilities to optimize the inlet boundary condition related to a physical reality by changing smoothly the penalty parameter in the interval between the two extremes and to treat the complete closures of the channel.