Modeling vocal fold motion with a hydrodynamic semicontinuum model

Vocal fold (VF) motion is a fundamental process in voice production, and is also a challenging problem for numerical computation because the VF dynamics depend on nonlinear coupling of air flow with the response of elastic channels (VF), which undergo opening and closing, and induce internal flow separation. The traditional modeling approach makes use of quasisteady flow approximation or Bernoulli's law which ignores air compressibility, and is known to be invalid during VF opening. A hydrodynamic semicontinuum system for VF motion is presented. The airflow is modeled by a modified quasi-one-dimensional Euler system with coupling to VF velocity. The VF is modeled by a lumped two mass system with a built-in geometric condition on flow separation. The modified Euler system contains the Bernoulli's law as a special case, and is derivable from the two-dimensional compressible Navier-Stokes equations in the inviscid limit. The computational domain contains also solid walls next to VFs (flexible walls). It is shown numerically that several salient features of VFs are captured, especially transients such as the double peaks of the driving subglottal pressures at the opening and the closing stages of VF motion consistent with fully resolved two-dimensional direct simulations, and experimental data. The system is much simpler to compute than a VF model based on two-dimensional Navier-Stokes system.