Finite elements in vocal tract acoustics: Generation of vowels, diphthongs and sibilants

Most physics related to voice production takes place in our larynx and in our vocal tract. In this work we will focus on the latter and show its role in the generation of vowels, diphthongs and sibilants. A review will be made of the involved partial differential equations and the finite element methods (FEM) used to solve them. These equations may range from the irreducible wave equation in the case of vowels, to its mixed formulation in an Arbitrary Eulerian-Lagrangian (ALE) framework in the case of diphthongs, or to the incompressible Navier-Stokes equations, which are solved to obtain the acoustic source terms of acoustic analogies in the numerical generation of sibilants. Yet, it is well-known that for mixed problems in general, the standard Galerkin FEM suffers from oscillations which make necessary to resort to some kind of numerical stabilization. The variational multiscale methods (VMM), also often referred to as subgrid scale stabilization (SGS) methods, offer a nice way out to this situation by splitting the problem unknowns into large scales, resolvable by the computational mesh, and small scales whose effects onto the large ones have to be modeled. The additional terms in the variational equations arising from the modeled subscales not only account for stabilization but also offer many other advantages that will be outlined in the present work. As regards the numerical examples, three-dimensional simulations of vowels and diphthongs will be presented, as well as a simulation on sound generated by flow past a sharp edge at the exit of a rectangular duct, which is important for understanding some basic features of sibilant production.