Finite elements in vocal tract acoustics generation of vowels.

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.