This thesis presents a method for fluid-structure interaction in a simplified 2D model of the human larynx using the arbitrary Lagrangian–Eulerian (ALE) approach and a strictly stable high order finite difference method. The ALE method is first tested for the fluid solver with a prescribed boundary movement, and then the method is extended to a two-way coupled explicit fluid-structure interaction where the vocal folds interact with the airflow in the larynx.
In each case, the fluid is treated as a Newtonian fluid obeying the perfect gas law and laminar flow is always assumed. Since the interest is ultimately phonation, the compressible Navier–Stokes equations are solved in order to resolve both the flow field and the acoustic waves. Characteristic-based non-reflecting boundary conditions are used so that no unphysical reflections occur at the outflow boundary of the limited computational domain.
The finite difference method relies on the summation by parts (SBP) technique which allows energy estimates to be made for the discretized equations in an analogous way as for the continuous problem. In the interior, the difference operator corresponds to the standard sixth order explicit difference method and is third order accurate near the boundaries. The classical explicit fourth order Runge–Kutta method is used for time integration.
For the structure field, the linear elastic wave equation is formulated as a first order system. The spatial derivatives are discretized by the same high order difference operator as employed for the flow equations. To implement boundary conditions for displacement or traction, a simultaneous approximation term (SAT) method is derived. Verification proves that the method is nearly fourth order accurate. The linear model is then extended to a nonlinear hyperelastic model based on a neo-Hookean constitutive relation. The strict energy estimate is only valid for the linear equation, but the SAT approach provides a consistent way to implement the traction boundary condition also for the nonlinear equations.
Fluid-structure interaction simulations are performed with model parameters corresponding to the real geometry of the human larynx and physical properties of the human vocal folds. Results for the vortex dynamics are investigated and preliminary acoustic results are obtained.