Three-dimensional (3D) numerical simulations of the vocal tract acoustics require very detailed vocal tract geometries in order to generate good quality vowel sounds. These geometries are typically obtained from Magnetic Resonance Imaging (MRI), from which a volumetric representation of the complex vocal tract shape is obtained. Static vowel sounds can then be generated using a finite element code, which simulates the propagation of acoustic waves through the vocal tract when a given train of glottal pulses is introduced at the glottal cross-section. A more challenging problem to solve is that of generating dynamic vowel sounds. On the one hand, the acoustic wave equation has to be solved in a computational domain with moving boundaries, which entails some numerical difficulties. On the other hand, the finite element meshes where acoustic wave propagation is computed have to move according to the dynamics of these very complex vocal tract shapes. In this work this problem is addressed. First, the acoustic wave equation in mixed form is expressed in an Arbitrary Lagrangian-Eulerian (ALE) framework to account for the vocal tract wall motion. This equation is numerically solved using a stabilized finite element approach. Second, the dynamic 3D vocal tract geometry is approximated by a finite set of cross-sections with complex shape. The time-evolution of these cross-sections is used to move the boundary nodes of the finite element meshes, while inner nodes are computed through diffusion. Some dynamic vowel sounds are presented as numerical examples.
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