Fluid-Structure Interaction

Larynx and vocal folds
2D model of larynx and vocal folds.

Numerical Simulation of Fluid-Structure Interaction in Human Phonation

Fluid-structure interaction in a simplified two-dimensional model of the larynx is considered in order to study human phonation. The flow is driven by an imposed pressure gradient across the glottis and interacts with the moving vocal folds in a self-sustained oscillation. The flow is computed by solving the 2D compressible Navier-Stokes equations using a high order finite difference method, which has been constructed to be strictly stable for linear hyperbolic and parabolic problems. The motion of the vocal folds is obtained by integrating the elastodynamic equations with a neo-Hookean constitutive model using a similar high order difference method as for the flow equations. Fluid and structure interact in a two-way coupling. In each time step at the fluid-structure interface, the structure provides the fluid with new no-slip boundary conditions and new grid velocities, and the fluid provides the structure with new traction boundary conditions. Algorithm
Algorithm for fluid-structure interaction.

Figures and animations of results may be found at Martin Larsson's former homepage.

Penalty Boundary Conditions for Elastodynamic Equations

Penalty boundary conditions based on simultaneous approximation terms (SAT) have been derived for the 2D linear elastic wave equation. They have been used to impose velocity and traction boundary conditions in the first order hyperbolic system corresponding to the linear elastic wave equation. For the spatial derivatives discretized by fourth order summation by parts (SBP) operators, fourth order convergence has been verified for test problems. This approach has been used to impose the traction boundary conditions for the fluid-structure interaction in human phonation.

References

    Larsson, M., Müller, B.: "Numerical Simulation of Fluid-Structure Interaction in Human Phonation", in: Skallerud, B., Andersson, H.I. (Eds.), MekIT'09, Fifth National Conference on Computational Mechanics, Trondheim, Norway, 26-27 May 2009, pp. 261-280. (pdf)
    Larsson, M., Müller, B.: "High Order Numerical Simulation of Fluid-Structure Interaction in Human Phonation", in: Pereira, J.C.F., Sequeira, A, Pereira, J.M.C. (Eds.), Proceedings of 5th ECCOMAS CFD Conference 2010, Lisbon, Portugal 14-17 June 2010, 17 pages. (pdf)
    Larsson, M., Müller, B.: "Numerical Simulation of Fluid-Structure Interaction in Human Phonation: Verification of Structure Part", in: J.S. Hesthaven and E.M. Rønquist (eds), Spectral and High Order Methods for Partial Differential Equations, Springer-Verlag, Berlin, Lecture Notes in Computational Science and Engineering, 2011, Volume 76, pp. 229-236, (DOI).
    Larsson, M., Müller, B.: "Numerical Simulation of Fluid-Structure Interaction in Human Phonation: Application", in: G. Kreiss, P. Lötstedt, A. Målqvist and M. Neytcheva (eds), Numerical Mathematics and Advanced Applications 2009, Part 2, Springer-Verlag, Berlin, 2010, pp. 571-578, (DOI).
    Larsson, M.: "Numerical Modeling of Fluid-Structure Interaction in the Human Larynx", PhD Thesis, Norwegian University of Science and Technology (NTNU), Trondheim, Norway, 2010. (Link).
    Larsson, M., Müller, B.: "High Order Numerical Simulation of Fluid-Structure Interaction in the Human Larynx", Proceedings of 8th International Conference on CFD in Oil & Gas, Metallurgical and Process Industries, SINTEF/NTNU, Trondheim, Norway, 21-23 June 2011, Paper CFD11-096, 10 pages. (pdf)

Contact

Bernhard Müller
Department of Energy and Process Engineering,
NTNU, Kolbjørn Hejes vei 2, NO-7491 Trondheim, Norway
http://folk.ntnu.no/bmuller/
Last modified: August 24, 2011
bernhard.muller(at)ntnu.no