Numerical solution of compressible and incompressible unsteady flows in channel inspired by vocal tract

This study deals with the numerical solution of a 2D unsteady flow of a viscous fluid in a channel for low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes, nearly closing the channel during oscillations. The channel is a simplified model of the glottal space in the human vocal tract. Four governing systems are considered to describe the unsteady laminar flow of a viscous fluid in the channel. The numerical solution is implemented using the finite volume method (FVM) and the predictor–corrector MacCormack scheme with artificial viscosity using a grid of quadrilateral cells. The unsteady grid of quadrilateral cells is considered in the form of conservation laws using the Arbitrary Lagrangian–Eulerian method. The numerical simulations of flow fields in the channel, acquired from a developed program, are presented for inlet velocity ${\hat{u}}_{\infty }=4.12m{s}^{‐1}$ and Reynolds number ${\mathrm{Re}}_{\infty }=4481$ and the wall motion frequency 100 Hz.