A New Model for Acoustic Wave Propagation and Scattering in the Vocal Tract

A new and efficient numerical model is proposed for simulating the acoustic wave propagation and scattering problems due to a complex geometry. In this model, the linearized Euler equations are solved by the finite-difference time-domain (FDTD) method on an orthogonal Eulerian grid. The complex wall boundary represented by a series of Lagrangian points is numerically treated by the immersed boundary method (IBM). To represent the interaction between these two systems, a force field is added to the momentum equation, which is calculated on the Lagrangian points and interpolated to the nearby Eulerian points. The pressure and velocity fields are then calculated alternatively using FDTD. The developed model is verified in the case of acoustic scattering by a cylinder, for which the exact solutions exist. The model is then applied to sound wave propagation in a 2D vocal tract with area function extracted from MRI data. To show the advantage of present model, the grid points are non-aligned with the boundary. The numerical results have good agreements with solutions in literature. A FDTD calculation with boundary condition directly imposed on the grid points closest to the wall cannot give a reasonable solution.