A new flow-structure interaction method is presented, which couples a sharp-interface immersed boundary method flow solver with a finite-element method based solid dynamics solver. The coupled method provides robust and high-fidelity solution for complex flow-structure interaction (FSI) problems such as those involving three-dimensional flow and viscoelastic solids. The FSI solver is used to simulate flow-induced vibrations of the vocal folds during phonation. Both two- and three-dimensional models have been examined and qualitative, as well as quantitative comparisons, have been made with established results in order to validate the solver. The solver is used to study the onset of phonation in a two-dimensional laryngeal model and the dynamics of the glottal jet in a three-dimensional model and results from these studies are also presented.

1.
Dumont
,
K.
,
Stijnen
,
J. M. A.
,
Vierendeels
,
J.
,
van de Vosse
,
F. N.
, and
Verdonck
,
P. R.
, 2004, “
Validation of a Fluid-Structure Interaction Model of a Heart Valve Using the Dynamic Mesh Method in Fluent
,”
Comput. Methods Biomech. Biomed. Eng.
1025-5842,
7
(
3
), pp.
139
146
.
2.
Einstein
,
D. R.
,
Kunzelman
,
K. S.
,
Reinhall
,
P. G.
,
Nicosia
,
M. A.
, and
Cochran
,
R. P.
, 2005, “
Non-Linear Fluid-Coupled Computational Model of the Mitral Valve
,”
J. Heart Valve Dis.
0966-8519,
14
(
3
), pp.
376
385
.
3.
Einstein
,
D. R.
,
del Pin
,
F.
,
Kunzelman
,
K.
,
Xiangmin
,
J.
,
Kuprat
,
A. P.
,
Carson
,
J. P.
,
Guccione
,
J. M.
, and
Ratcliffe
,
M. B.
, 2010, “
Fluid-Structure Interactions of the Mitral Valve and Left Heart: Comprehensive Strategies, Past, Present and Future
,”
Int. J. Numer. Methods Biomed. Eng.
,
26
, pp.
348
380
.
4.
Guivier
,
C.
,
Deplano
,
V.
, and
Pibarot
,
P.
, 2007, “
New Insights Into the Assessment of the Prosthetic Valve Performance in the Presence of Subaortic Stenosis Through a Fluid-Structure Interaction Model
,”
J. Biomech.
0021-9290,
40
(
10
), pp.
2283
2290
.
5.
Kaminsky
,
R.
,
Dumont
,
K.
,
Weber
,
H.
,
Schroll
,
M.
, and
Verdonck
,
P.
, 2007, “
PIV Validation of Blood-Heart Valve Leaflet Interaction Modeling
,”
Int. J. Artif. Organs
0391-3988,
30
(
7
), pp.
640
648
.
6.
Morsi
,
Y. S.
,
Yang
,
W. W.
,
Wong
,
G. S.
, and
Das
,
S.
, 2007, “
Transient Fluid-Structure Coupling for Simulation of a Trileaflet Heart Valve Using Weak Coupling
,”
Int. J. Artif. Organs
0391-3988,
10
(
2
), pp.
96
103
.
7.
Weinberg
,
E. J.
, and
Kaazempur Mofrad
,
M. R.
, 2007, “
Transient, Three-Dimensional, Multiscale Simulations of the Human Aortic Valve
,”
Cardiovasc. Eng.
1567-8822,
7
(
4
), pp.
140
155
.
8.
Peskin
,
C. S.
, 1972, “
Flow Patterns Around Heart Valve: A Digital Computer Method for Solving the Equations of Motion
,” Ph.D. thesis, Albert Einstein College of Medicine, Bronx, NY.
9.
Borazjani
,
R.
,
Ge
,
L.
, and
Sotiropoulos
,
F.
, 2008, “
Curvilinear Immersed Boundary Method for Simulating Fluid Structure Interaction With Complex 3D Rigid Body
,”
J. Comput. Phys.
0021-9991,
227
, pp.
7587
7620
.
10.
De Hart
,
J.
,
Peters
,
G. W.
,
Schreurs
,
P. J.
, and
Baaijens
.
F. P.
, 2003, “
A Three-Dimensional Computational Analysis of Fluid-Structure Interaction in the Aortic Valve
,”
J. Biomech.
0021-9290,
36
(
1
), pp.
103
112
.
11.
Mittal
,
R.
, and
Iaccarino
,
G.
, 2005, “
Immersed Boundary Methods
,”
Annu. Rev. Fluid Mech.
0066-4189,
37
, pp.
239
261
.
12.
van Loon
,
R.
,
Anderson
,
P. D.
, and,
van de Vosse
,
F. N.
, 2006, “
A Fluid–Structure Interaction Method With Solid-Rigid Contact for Heart Valve Dynamics
,”
J. Comput. Phys.
0021-9991,
217
(
2
), pp.
806
823
.
13.
van Loon
,
R.
,
Anderson
,
P. D.
,
de Hart
,
J.
, and
Baaijens
,
F. P. T.
, 2004, “
A Combined Fictitious Domain/Adaptive Meshing Method for Fluid-Structure Interaction in Heart Valves
,”
Int. J. Numer. Methods Fluids
0271-2091,
46
(
5
), pp.
533
544
.
14.
Watton
,
P.
,
Luo
,
X. Y.
,
Yin
,
M.
,
Bernacca
,
G. M.
, and
Wheatley
,
D. J.
, 2008, “
Effect of Ventricle Motion on the Dynamic Behavior of Chorded Mitral Valves
,”
J. Fluids Struct.
0889-9746,
24
, pp.
58
74
.
15.
Watton
,
P. N.
,
Luo
,
X. Y.
,
Wang
,
X.
,
Bernacca
,
G. M.
,
Molloy
,
P.
, and
Wheatley
,
D. J.
, 2007, “
Dynamic Modelling of Prosthetic Chorded Mitral Valves Using the Immersed Boundary Method
,”
J. Biomech.
0021-9290,
40
(
3
), pp.
613
626
.
16.
Mittal
,
R.
,
Dong
,
H.
,
Bozkurttas
,
M.
,
Najjar
,
F. M.
,
Vargas
,
A.
, and
von Loebbecke
,
A.
, 2008, “
A Versatile Sharp Interface Method for Incompressible Flows With Complex Boundaries
,”
J. Comput. Phys.
0021-9991,
227
(
10
), pp.
4825
4852
.
17.
Luo
,
H.
,
Mittal
,
R.
,
Zheng
,
X.
,
Bielamowicz
,
S. A.
,
Walsh
,
R. J.
, and
Hahn
,
J. K.
, 2008, “
An Immersed-Boundary Method for Flow-Structure Interaction in Biological Systems With Application to Phonation
,”
J. Comput. Phys.
0021-9991,
227
, pp.
9303
9332
.
18.
Zhao
,
H.
,
Freund
,
J. B.
, and
Moser
,
R. D.
, 2008, “
A Fixed-Mesh Method of for Incompressible Flow-Structure Systems With Finite Solid Deformations
,”
J. Comput. Phys.
0021-9991,
227
, pp.
3114
3140
.
19.
Hirano
,
M.
, 1977, “
Structure and Vibratory Behavior of the Vocal Folds
,”
Dynamic Aspect of Speech Production
,
University of Tokyo Press
,
Tokyo, Japan
.
20.
Belytschko
,
T.
,
Liu
,
W.
, and
Moran
,
B.
, 2000,
Nonlinear Finite Elements for Continua and Structures
,
Wiley
,
New York
.
21.
Van Kan
,
J.
, 1986, “
A Second-Order Accurate Pressure-Correction Scheme for Viscous Incompressible Flow
,”
SIAM J. Sci. Stat. Comput.
0196-5204,
7
(
3
), pp.
870
891
.
22.
Udaykumar
,
H. S.
,
Mittal
,
R.
,
Pampunggoon
,
P.
, and
Khanna
,
A.
, 2001, “
A Sharp Interface Cartesian Grid Method for Simulating Flows With Complex Moving Boundaries
,”
J. Comput. Phys.
0021-9991,
174
, pp.
345
380
.
23.
Fung
,
Y. C.
, 1993,
Biomechanics
, 2nd ed.,
Springer-Verlag
,
New York
.
24.
Cuthill
,
E.
, and
McKee
,
J.
, 1969, “
Reducing the Bandwidth of Sparse Symmetric Matrices
,”
Proceedings of the 24th National Conference ACM
, pp.
157
172
.
25.
Gibbs
,
N. E.
,
Poole
,
W. G.
, and
Stockmeyer
,
P. K.
, 1976, “
A Comparison of Several Bandwidth and Profile Reduction Algorithms
,”
ACM Trans. Math. Softw.
0098-3500,
2
(
4
), pp.
322
330
.
26.
Zheng
,
X.
, 2009, “
Biomechanical Modeling of Glottal Aerodynamics and Vocal Fold Vibration During Phonation
,” Ph.D. thesis, The George Washington University, Washington, DC.
27.
Ghias
,
R.
,
Mittal
,
R.
, and
Dong
,
H.
, 2007, “
A Shape Interface Immersed Boundary Method for Compressible Viscous Flow
,”
J. Comput. Phys.
0021-9991,
225
(
1
), pp.
528
553
.
28.
Batchelor
,
G. K.
, 2000,
An Introduction to Fluid Dynamics
,
Cambridge University Press
,
Cambridge, UK
.
29.
Ishizaka
,
K.
, and
Flanagan
,
J. L.
, 1972, “
Synthesis of Voiced Sounds From a Two-Mass Model of the Vocal Cords
,”
Bell Syst. Tech. J.
0005-8580,
51
(
6
), pp.
1233
1268
.
30.
Ishizaka
,
K.
, 1981, “
Equivalent Lumped-Mass Models of Vocal Fold
,”
Vocal Fold Physiology
,
University of Tokyo Press
,
Tokyo, Japan
, pp.
231
241
.
31.
Story
,
B. H.
, and
Titze
,
I. R.
, 1995, “
Voice Simulation With a Body-Cover Model of the Vocal Folds
,”
J. Acoust. Soc. Am.
0001-4966,
97
(
2
), pp.
1249
1260
.
32.
Titze
,
I. R.
, 1973, “
The Human Vocal Cords: A Mathematical Model: Part I
,”
Phonetica
0031-8388,
28
, pp.
129
170
.
33.
Guo
,
C. -G.
, and
Scherer
,
R. C.
, 1993, “
Finite Element Simulation of Glottal Flow and Pressure
,”
J. Acoust. Soc. Am.
0001-4966,
94
(
2
), pp.
688
700
.
34.
Zhang
,
C.
,
Zhao
,
W.
,
Frankel
,
S.
, and
Mongeau
,
L.
, 2002, “
Computational Aeroacoustics of Phonation, Part II: Effects of Flow Parameters and Ventricular Folds
,”
J. Acoust. Soc. Am.
0001-4966,
112
(
5
), pp.
2147
2154
.
35.
Zhao
,
W.
,
Zhang
,
C.
,
Frankel
,
S.
, and
Mongeau
,
L.
, 2002, “
Computational Aeroacoustics of Phonation, Part I: Computational Methods and Sound Generation Mechanisms
,”
J. Acoust. Soc. Am.
0001-4966,
112
(
5
), pp.
2134
2146
.
36.
Alipour
,
F.
,
Berry
,
D. A.
, and
Titze
,
I. R.
, 2000, “
A Finite-Element Model of Vocal-Fold Vibration
,”
J. Acoust. Soc. Am.
0001-4966,
108
(
6
), pp.
3003
3012
.
37.
Cook
,
D. D.
,
Nauman
,
E.
, and
Mongeau
,
L.
, 2008, “
Reducing the Number of Vocal Fold Mechanical Tissue Properties: Evaluation of the Incompressibility and Planar Displacement Assumptions
,”
J. Acoust. Soc. Am.
0001-4966,
124
(
6
), pp.
3888
3896
.
38.
Tao
,
C.
, and
Zhang
,
Y.
,
Hottinger
,
D. G.
, and
Jiang
,
J. J.
, 2007,“
Asymmetric Airflow and Vibration Induced by the Coanda Effect in a Symmetric Model of the Vocal Folds
,”
J. Acoust. Soc. Am.
0001-4966,
122
(
4
), pp.
2270
2278
.
39.
Zheng
,
X.
,
Bielamowicz
,
S.
,
Luo
,
H.
, and
Mittal
,
R.
, 2009, “
Computational Study of the Effect of False Vocal Folds on Glottal Flow on Vocal Fold Vibration During Phonation
,”
Ann. Biomed. Eng.
0090-6964,
37
(
3
), pp.
625
642
.
40.
Herzel
,
H.
,
Berry
,
D.
, and
Titze
,
I. R.
, 1994, “
Analysis of Vocal Disorders With Methods From the Nonlinear Dynamics
,”
J. Speech Hear. Res.
0022-4685,
37
, pp.
1008
1019
.
41.
Baer
,
T.
, 1975, “
Investigation of Phonation Using Excised Larynges
,” Ph.D. thesis, Massachusetts of Technology, Cambridge, MA.
42.
Titze
,
I. R.
,
Schmidt
,
S. S.
, and
Titze
,
M. R.
, 1995, “
Phonation Threshold Pressure in a Physical Model of the Vocal Fold Mucosa
,”
J. Acoust. Soc. Am.
0001-4966,
97
(
5
), pp.
3080
3084
.
43.
Alipour
,
F.
,
Jaiswal
,
S.
, and
Finnegan
,
E.
, 2007, “
Aerodynamic and Acoustic Effects of False Vocal Folds and Epiglottis in Excised Larynx Models
,”
Ann. Otol. Rhinol. Laryngol.
0003-4894,
116
(
2
), pp.
135
144
.
44.
Erath
,
B. D.
, and
Plesniak
,
M. W.
, 2006, “
An Investigation of Bimodal Jet Trajectory in Flow Through Scaled Models of the Human Vocal Tract
,”
Exp. Fluids
0723-4864,
40
, pp.
683
696
.
45.
Neubauer
,
J.
, and
Zhang
,
Z.
, 2007, “
Coherent Structures of the Near Field Flow in a Self-Oscillating Physical Model of the Vocal Folds
,”
J. Acoust. Soc. Am.
0001-4966,
121
(
2
), pp.
1102
1118
.
46.
Triep
,
M.
,
Brücker
,
Ch.
, and
Schröder
,
W.
, 2005, “
High-Speed PIV Measurements of the Flow Downstream of a Dynamic Mechanical Model of the Human Vocal Folds
,”
Exp. Fluids
0723-4864,
39
, pp.
232
245
.
47.
Titze
,
I. R.
, 1994, “
Mechanical Stress in Phonation
,”
J. Voice
0892-1997,
8
(
2
), pp.
99
105
.
48.
Chong
,
M. S.
, and
Perry
,
A. E.
, 1990, “
A General Classification of Three-Dimensional Flow Fields
,”
Phys. Fluids A
0899-8213,
2
, pp.
765
777
.
49.
Hussain
,
A. K. M. F.
, and
Reynolds
,
W. C.
, 1975, “
Measurements in Fully Developed Turbulent Channel Flow
,”
ASME J. Fluids Eng.
0098-2202,
97
, pp.
568
580
.
50.
Mittal
,
R.
,
Simmons
,
S. P.
, and
Najjar
,
F.
, 2003, “
Numerical Study of Pulsatile Flow in a Constricted Channel
,”
J. Fluid Mech.
0022-1120,
485
, pp.
337
378
.
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