High order numerical simulation of fluid-structure interaction in the human larynx

Bernhard Müller
Department of Energy and Process Engineering
Norwegian University of Science and Technology
Trondheim, Norway


To gain insight into phonation, we have developed a 2D model able to capture the effect of self-sustained oscillations of vocal fold tissue in the human larynx due to the interaction with the airflow from the lungs. Since we are interested in the generation and propagation of sound in the airways, we model the flow by the compressible Navier-Stokes equations. In order to obtain the energy estimate required for strict stability, the solver utilizes sixth order accurate summation by parts finite difference operators in space, which are third order accurate near the boundaries. The classical fourth order explicit Runge-Kutta method is employed in time.

For the structure part of the simulation, we use the linear elastic wave equation as well as the nonlinear Lagrangean field equations for a compressible neo-Hookean hyperelastic material. The equations are expressed as a first order hyperbolic system and solved similarly as the flow equations.

The velocities and displacements obtained from the structure solver at the fluid-structure interface are used in every time step to impose boundary conditions for the flow solver by employing the arbitrary Lagrangian-Eulerian (ALE) approach. The flow solution provides the structure solver with new traction boundary conditions, which are imposed by the simultaneous approximation term (SAT) approach.

We have performed simulations for the coupled fluid-structure system with realistic parameters for human phonation. We have been able to model the self-sustained oscillations at the expected frequency.