# 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

### Abstract:

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.