In order to analyze the fluid-structure interaction between a flow and a flexible structure, an algorithm was presented to couple the lattice Boltzmann method (LBM) and the finite element method (FEM). The LBM was applied to the fluid dynamics while the FEM was applied to the structural dynamics. The two solution techniques were solved in a staggered manner, i.e., one solver after another. Continuity of the velocity and traction was applied at the interface boundaries between the fluid and structural domains. Furthermore, so as to make the fluid-structure interface boundary more flexible in terms of the computational modeling perspective, a technique was also introduced for the LBM so that the interface boundary might not coincide with the fluid lattice mesh. Some example problems were presented to demonstrate the developed techniques.

1.
Zienkiewicz
,
O. C.
, and
Newton
,
R. E.
, 1969, “
Coupled Vibration of a Structure Submerged in a Compressible fluid
,”
Proceedings of International Symposium on Finite Element Techniques
,
Stuttgart
, May, 1–15.
2.
Zienkiewicz
,
O. C.
,
Onate
,
E.
, and
Heinrich
,
J. C.
, 1981, “
A General Formulation for Coupled Thermal Flow of Metals Using Finite Elements
,”
Int. J. Numer. Methods Eng.
0029-5981,
17
, pp.
1497
1514
.
3.
Lewis
,
R. W.
,
Bettess
,
P.
, and
Hinton
,
E.
, 1984,
Numerical Methods in Coupled Systems
,
Wiley
,
Chichester
.
4.
Kwon
,
Y. W.
, and
Fox
,
P. K.
, 1993, “
Underwater Shock Response of a Cylinder Subjected to a Side on Explosion
,”
Comput. Struct.
0045-7949,
48
(
4
), pp.
637
646
.
5.
Kwon
,
Y. W.
,
Bergensen
,
J. K.
, and
Shin
,
Y. S.
, 1994, “
Effect of Surface Coatings on Cylinders Exposed to Underwater Shock
,”
Shock Vib.
1070-9622,
1
(
3
), pp.
637
646
.
6.
Kwon
,
Y. W.
, and
Cunningham
,
R. E.
, 1998, “
Comparison of USA-DYNA Finite Element Models for a Stiffened Shell Subject to Underwater Shock
,”
Comput. Struct.
0045-7949,
66
(
1
), pp.
127
144
.
7.
Newton
,
R. E.
, 1980, “
Finite Element Study of Shock Induced Cavitation
,”
ASCE Spring Conference
,
Portland, OR
.
8.
Zienkiewicz
,
O. C.
,
Paul
,
D. K.
, and
Hinton
,
E.
, 1983, “
Cavitation in Fluid-Structure Response With Particular Reference to Dam Under Earthquake Loading
,”
Earthquake Eng. Struct. Dyn.
0098-8847,
11
, pp.
463
381
.
9.
Bathe
,
K. J.
,
Nitikipaiboon
,
C.
, and
Wang
,
X.
, 1995, “
A Mixed Displacement-Based Finite Element Formulation for Acoustice Fluid-Structure Interaction
,”
Comput. Struct.
0045-7949,
56
, pp.
225
237
.
10.
Kwon
,
Y. W.
, and
McDermott
,
P. M.
, 2001, “
Effects of Void Growth and Nucleation on Plastic Deformation of Plates Subjected to Fluid-Structure Interaction
,”
ASME J. Pressure Vessel Technol.
0094-9930,
123
, PP.
480
485
.
11.
Everstine
,
G. C.
, and
Henderson
,
F. M.
, 1990, “
Coupled Finite Element∕Boundary Element Approach for Fluid-Structure Interaction
,”
J. Acoust. Soc. Am.
0001-4966,
87
, pp.
1938
1947
.
12.
Giordano
,
J. A.
, and
Koopmann
,
G. H.
, 1995, “
State Space Boundary Element-Finite Element Coupling for Fluid-Structure Interaction Analysis
,”
J. Acoust. Soc. Am.
0001-4966,
98
, pp.
363
372
.
13.
Dubini
,
G.
,
Pietrabissa
,
R.
, and
Montevecchi
,
F. M.
, 1995, “
Fluid-Structure Interaction Problems in Bio-Fluid Mechanics: A Numerical Study of the Motion of an Isolated Particle Freely Suspended in Channel Flow
,”
Med. Eng. Phys.
1350-4533,
17
, pp.
609
617
.
14.
Tienfuan
,
K.
,
Lee
,
L. L.
, and
Wellford
,
L. C.
, 1997, “
Transient Fluid-Structure Interaction in a Control Valve
,”
ASME Trans. J. Fluids Eng.
0098-2202,
119
, pp.
354
359
.
15.
MvNamara
,
G.
, and
Zenetti
,
G.
, 1988, “
Use of the Boltzmann Equation to Simulate Lattice-Gas Automata
,”
Phys. Rev. Lett.
0031-9007,
61
, pp.
2332
2335
.
16.
Qian
,
Y. H.
, 1993, “
Simulating Thermodynamics With Lattice BKG Models
,”
J. Sci. Comput.
0885-7474,
8
, pp.
231
241
.
17.
Chen
,
H.
, 1993, “
Discrete Boltzmann Systems and Fluid Flows
,”
Comput. Phys.
0894-1866,
7
, pp.
632
637
.
18.
Cali
,
A.
,
Succi
,
S.
,
Cancelliere
,
A.
,
Benzi
,
R.
, and
Gramingnani
,
M.
, 1992, “
Diffusion and Hydrodynamic Dispersion With the Lattice Boltzmann Method
,”
Phys. Rev. A
1050-2947,
45
, pp.
5771
5774
.
19.
Chen
,
S.
, and
Doolen
,
G. D.
, 1998, “
Lattice Boltzmann Method for Fluid Flow
,”
Annu. Rev. Fluid Mech.
0066-4189,
30
, pp.
329
364
.
20.
Flekkoy
,
E. G.
, 1993, “
Lattice Bhatnagar-Gross-Krook Models for Miscible Fluids
,”
Phys. Rev. E
1063-651X,
47
, pp.
4247
4257
.
21.
Swift
,
M. R.
,
Orlandini
,
E.
,
Osborn
,
W. R.
, and
Yeomans
,
J. M.
, 1996, “
Lattice Boltzmann Simulations of Liquid-Gas and the Binary Fluid Systems
,”
Phys. Rev. E
1063-651X,
54
, pp.
5041
5052
.
22.
Soe
,
M.
,
Vahala
,
G.
,
Pavlo
,
P.
,
Vahala
,
L.
,
Chen
,
H.
, 1998, “
Thermal Lattice Boltzmann Simulations of Variable Prandtl Number Turbulent Flows
,”
Phys. Rev. E
1063-651X,
57
, pp.
4227
4237
.
23.
Peng
,
Y.
,
Shu
,
C.
, and
Chew
,
Y. T.
, 2003, “
Simplified Thermal Lattice Boltzmann Model for Incompressible Thermal Flows
,”
Phys. Rev. E
1063-651X,
68
, p.
026701
.
24.
Krafczyk
,
M.
,
Tolke
,
J.
,
Rank
,
E.
, and
Schulz
,
M.
, 2001, “
Two-Dimensional Simulation of Fluid-Structure Interaction Using Lattice-Boltzmann Methods
,”
Comput. Struct.
0045-7949,
79
, pp.
2031
2037
.
25.
Frisch
,
U.
,
Hasslacher
,
B.
, and
Pomeau
,
Y.
, 1986, “
Lattice-Gas automata for the Navier–Stokes Equations
,”
Phys. Rev. Lett.
0031-9007,
56
, pp.
1505
1508
.
26.
Bhatnagar
,
P.
,
Bross
,
E. P.
, and
Krook
,
M. K.
, 1954, “
A Model for Collision Process in Gases. I: Small Amplitude Processes in Charged and Neutral One-Component System
,”
Phys. Rev.
0031-899X,
94
, pp.
511
525
.
27.
Peng
,
G.
,
Xi
,
H.
, and
Duncan
,
C.
, 1998, “
Lattice Boltzmann Method on Irregular Meshes
,”
Phys. Rev. E
1063-651X,
58
, pp.
R4124
R4127
.
28.
Xi
,
H.
,
Peng
,
G.
, and
Chou
,
S.-H.
, 1999, “
Finite-Volume Lattice Boltzmann Method
,”
Phys. Rev. E
1063-651X,
59
, pp.
6202
6205
.
29.
Newmark
,
N. M.
, 1959, “
A Method of Computation for Structural Dynamics
,”
J. Engrg. Mech. Div.
0044-7951,
85
, pp.
67
94
.
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