In this study, a combination of the smoothed particle hydrodynamics (SPH) and finite element method (FEM) solving the complex problem of interaction between fluid with free surface and an elastic structure is studied. A brief description of SPH and FEM is presented. Contact mechanics is used for the coupling between fluid and structure, which are simulated with SPH and FEM, respectively. In the proposed method, to couple mesh-free and mesh-based methods, fluid and structure are solved together by a complete stiffness matrix instead of iterative predictive–corrective or master–slave methods. In addition, fully dynamic large-deformation analysis is carried out in FEM by taking into account mass and damping of the elastic structure. Accordingly, a two-dimensional fluid–structure interaction (FSI) code is developed and validated with two different experiments available in the literature. The results of the numerical method are in good agreement with the experiments. In addition, a novel laboratory experiment on a dam break problem with elastic gate in which the length of the initial water column is larger than its height is conducted. The main difference between the previous experiments and the one conducted in this study is that an upward water motion parallel to the elastic gate is observed at the upstream side of the gate. This motion is captured with the numerical method.

References

References
1.
Bathe
,
K.
,
Zhang
,
H.
, and
Ji
,
S.
,
1999
, “
Finite Element Analysis of Fluid Flows Fully Coupled With Structural Interactions
,”
Comput. Struct.
,
72
(
1–3
), pp.
1
16
.
2.
Dowell
,
E. H.
, and
Hall
,
K. C.
,
2001
, “
Modeling of Fluid–Structure Interaction
,”
Annu. Rev. Fluid Mech.
,
33
(
1
), pp.
445
490
.
3.
Ohayon
,
R.
, and
Felippa
,
C. E.
,
2001
, “
Advances in Computational Methods for Fluid–Structure Interaction and Coupled Problems
,”
Comput. Methods Appl. Mech. Eng.
,
190
(
24–25
), pp.
2977
3292
.
4.
Tezduyar
,
T.
, and
Bazilevs
,
Y.
,
2008
, “
Fluid–Structure Interaction
,”
Comput. Mech.
,
43
(
1
), pp.
1
189
.
5.
Gingold
,
R. A.
, and
Monaghan
,
J. J.
,
1977
, “
Smoothed Particle Hydrodynamics: Theory and Application to Non-Spherical Stars
,”
Mon. Not. R. Astron. Soc.
,
181
(
3
), pp.
375
389
.
6.
Lucy
,
L. B.
,
1977
, “
A Numerical Approach to the Testing of the Fission Hypothesis
,”
Astron. J.
,
82
(
12
), p.
1013
.
7.
Monaghan
,
J.
,
1994
, “
Simulating Free Surface Flows With SPH
,”
J. Comput. Phys.
,
110
(
2
), pp.
399
406
.
8.
Monaghan
,
J.
, and
Kocharyan
,
A.
,
1995
, “
SPH Simulation of Multi-Phase Flow
,”
Comput. Phys. Commun.
,
87
(
1–2
), pp.
225
235
.
9.
Chaussonnet
,
G. G.
,
Koch
,
R. R.
,
Bauer
,
H. J.
,
Sänger
,
A. A.
,
Jakobs
,
T. T.
, and
Kolb
,
T. T.
,
2018
, “
Smoothed Particle Hydrodynamics Simulation of an Air-Assisted Atomizer Operating at High Pressure: Influence of Non-Newtonian Effects
,”
ASME. J. Fluids Eng.
,
140
(
6
), p.
061301.
10.
Liu
,
Z.
, and
Liu
,
Z.
,
2017
, “
The Comparison of Viscous Force Approximations of Smoothed Particle Hydrodynamics in Poiseuille Flow Simulation
,”
ASME J. Fluids Eng.
,
139
(
5
), p.
051302
.
11.
Monaghan
,
J.
,
1995
,
Simulating Gravity Currents With SPH Lock Gates, Applied Mathematics Reports and Preprints
,
Monash University
, Melbourne, Australia.
12.
Chen
,
J. K.
,
Beraun
,
J. E.
, and
Carney
,
T. C.
,
1999
, “
A Corrective Smoothed Particle Method for Boundary Value Problems in Heat Conduction
,”
Int. J. Numer. Methods Eng.
,
46
(
2
), pp.
231
252
.
13.
Swegle
,
J.
,
Hicks
,
D.
, and
Attaway
,
S.
,
1995
, “
Smoothed Particle Hydrodynamics Stability Analysis
,”
J. Comput. Phys.
,
116
(
1
), pp.
123
134
.
14.
Benz
,
W.
, and
Asphaug
,
E.
,
1995
, “
Simulations of Brittle Solids Using Smooth Particle Hydrodynamics
,”
Comput. Phys. Commun.
,
87
(
1–2
), pp.
253
265
.
15.
Dinçer
,
A. E.
,
Bozkus
,
Z.
, and
Tijsseling
,
A. S.
,
2018
, “
Prediction of Pressure Variation at an Elbow Subsequent to a Liquid Slug Impact by Using Smoothed Particle Hydrodynamics
,”
ASME J. Pressure Vessel Technol.
,
140
(
3
), p.
031303
.
16.
Dinçer
,
A. E.
,
2017
, “
Numerical Investigation of Free-Surface and Pipe Flow Problems by Smoothed Particle Hydrodynamics
,” Ph.D. thesis, Middle East Technical University, Ankara, Turkey.
17.
Hosseinkhani
,
M.
, and
Omidvar
,
P.
,
2018
, “
Smoothed Particle Hydrodynamics for the Rising Pattern of Oil Droplets
,”
ASME J. Fluids Eng.
,
140
(
8
), p.
081105
.
18.
Horton
,
B.
,
Song
,
Y.
,
Feaster
,
J.
, and
Bayandor
,
J.
,
2017
, “
Benchmarking of Computational Fluid Methodologies in Resolving Shear-Driven Flow Fields
,”
ASME J. Fluids Eng.
,
139
(
11
), p.
111402
.
19.
Bathe
,
K.
, and
Chaudhary
,
A.
,
1985
, “
A Solution Method for Planar and Axisymmetric Contact Problems
,”
Int. J. Numer. Methods Eng.
,
21
(
1
), pp.
65
88
.
20.
Deuflhard
,
P.
,
Krause
,
R.
, and
Ertel
,
S.
,
2008
, “
A Contact-Stabilized Newmark Method for Dynamical Contact
,”
Numer. Methods Eng.
,
73
(
9
), pp.
1274
1290
.
21.
Chawla
,
V.
, and
Laursen
,
T.
,
1998
, “
Energy Consistent Algorithms for Frictional Contact Problems
,”
Int. J. Numer. Methods Eng.
,
42
(
5
), pp.
799
827
.
22.
Khenous
,
H. B.
,
Patrick
,
L.
, and
Renard
,
Y.
,
2006
, “
Comparison of Two Approaches for the Discretization of Elastodynamic Contact Problems
,”
Math. Probl. Mech.
,
342
, pp.
791
796
.
23.
Feng
,
Z. Q.
,
Magnain
,
B.
, and
Cros
,
J. M.
,
2006
, “
Solution of Large Deformation Impact Problems With Friction Between Blatz-Kohyperelastic Bodies
,”
Int. J. Eng. Sci.
,
44
(
1-2
), pp.
113
126
.
24.
Munjiza
,
A.
,
2004
,
The Combined Finite-Discrete Element Method
,
Wiley
, Chichester, UK.
25.
Attaway
,
S.
,
Heinstein
,
M.
, and
Swegle
,
J.
,
1994
, “
Coupling of Smooth Particle Hydrodynamics With the Finite Element Method
,”
Nucl. Eng. Des.
,
150
(
2–3
), pp.
199
205
.
26.
De Vuyst
,
T.
,
Vignjevic
,
R.
, and
Campbell
,
J. C.
,
2005
, “
Coupling Between Meshless and Finite Element Methods
,”
Int. J. Impact Eng.
,
31
(
8
), pp.
1054
1064
.
27.
Fernandez-Mendez
,
S.
,
Bonet
,
J.
, and
Huerta
,
A.
,
2005
, “
Continuous Blending of SPH With Finite Elements
,”
Comput. Struct.
,
83
, pp.
1448
1458
.
28.
Zang
,
Z.
,
Qiang
,
H.
, and
Gao
,
W.
,
2011
, “
Coupling of Smoothed Particle Hydrodynamics and Finite Element Method for Impact Dynamics Simulation
,”
Eng. Struct.
,
33
, pp.
255
264
.
29.
Fourey
,
G.
,
Oger
,
G.
,
Touzé
,
D. L.
, and
Alessandrini
,
B.
,
2010
, “
Violent Fluid-Structure Interaction Simulations Using a Coupled SPH/FEM Method
,”
IOP Conf. Ser.: Mater. Sci. Eng.
,
10
, p.
012041
.
30.
Groenenboom
,
P. H. L.
, and
Cartwright
,
B. K.
,
2010
, “
Hydrodynamics and Fluid-Structure Interaction by Coupled SPH-FE Method
,”
J. Hydraul. Res.
,
48
(
Suppl. 1
), pp.
61
73
.
31.
Hu
,
D.
,
Long
,
T.
,
Xiao
,
Y.
,
Han
,
X.
, and
Gu
,
Y.
,
2014
, “
Fluid–Structure Interaction Analysis by Coupled FE–SPH Model Based on a Novel Searching Algorithm
,”
Comput. Methods Appl. Mech. Eng.
,
276
, pp.
266
286
.
32.
Fourey
,
G.
,
Hermange
,
C.
,
Le Touzé
,
D.
, and
Oger
,
G.
,
2017
, “
An Efficient FSI Coupling Strategy Between Smoothed Particle Hydrodynamics and Finite Element Methods
,”
Comput. Phys. Commun.
,
217
, pp.
66
81
.
33.
Long
,
T.
,
Hu
,
D.
,
Wan
,
D.
,
Zhuang
,
C.
, and
Yang
,
G.
,
2017
, “
An Arbitrary Boundary With Ghost Particles Incorporated in Coupled FEM–SPH Model for FSI Problems
,”
J. Comput. Phys.
,
350
, pp.
166
183
.
34.
Demir
,
A.
,
Dinçer
,
A. E.
,
Bozkuş
,
Z.
, and
Tijsseling
,
A. S.
, 2019, “
Numerical and Experimental Investigation of Damping in a Dam-Break Problem With Fluid-Structure Interaction
,”
J. Zhejiang Univ., Sci. A
, (accepted manuscript).
35.
Swaddiwudhipong
,
S.
,
Islam
,
M.
, and
Liu
,
Z.
,
2010
, “
High Velocity Penetration/Perforation Using Coupled Smooth Particle Hydrodynamics-Finite Element Method
,”
Int. J. Prot. Struct.
,
1
(
4
), pp.
489
506
.
36.
Danilewicz
,
A.
, and
Sikora
,
Z.
,
2015
, “
Numerical Simulation of Crater Creating Process in Dynamic Replacement Method by Smooth Particle Hydrodynamics
,”
Stud. Geotech. Mech.
,
36
(
3
), pp.
3
8
.
37.
Fourtakas
,
G.
,
Vacondio
,
R.
, and
Rogers
,
B. D.
,
2015
, “
On the Approximate Zeroth and First-Order Consistency in the Presence of 2-D Irregular Boundaries in SPH Obtained by the Virtual Boundary Particle Methods
,”
Int. J. Numer. Methods Fluids
,
78
(
8
), pp.
475
501
.
38.
Liu
,
G. R.
, and
Liu
,
M. B.
,
2003
,
Smoothed Particle Hydrodynamics: A Mesh-Free Particle Method
,
World Scientific
,
Singapore
.
39.
Monaghan
,
J.
,
1989
, “
On the Problem of Penetration in Particle Methods
,”
J. Comput. Phys.
,
82
(
1
), pp.
1
15
.
40.
Hirsch
,
C.
,
1988
,
Numerical Computation of Internal and External Flows
, Vol.
1
,
Wiley-Interscience Publication
, Burlington, VT.
41.
Anderson
,
J. D.
,
1995
,
Computational Fluid Dynamics: The Basics With Applications
,
Mc Graw-Hill
, New York.
42.
Molteni
,
D.
, and
Colagrossi
,
A.
,
2009
, “
A Simple Procedure to Improve the Pressure Evaluation in Hydrodynamic Context Using the SPH
,”
Comput. Phys. Commun.
,
180
(
6
), pp.
861
872
.
43.
Bathe
,
K.
,
1982
,
Finite Element Procedures in Engineering Analysis
,
Prentice Hall
, Englewood Cliffs, NJ.
44.
Chopra
,
A. K.
,
2007
,
Dynamics of Structures: Theory and Applications to Earthquake Engineering
,
Pearson/Prentice Hall
,
Upper Saddle River, NJ
.
45.
Demir
,
A.
,
2017
, “
Multi Segment Continuous Cables With Frictional Contact Along Their Span
,” Ph.D. thesis, Middle East Technical University, Ankara, Turkey.
46.
Xu
,
R.
,
Stansby
,
P.
, and
Laurence
,
D.
,
2009
, “
Accuracy and Stability in Incompressible SPH (ISPH) Based on the Projection Method and a New Approach
,”
J. Comput. Phys.
,
228
(
18
), pp.
6703
6725
.
47.
Antoci
,
C.
,
Gallati
,
M.
, and
Sibilla
,
S.
,
2007
, “
Numerical Simulation of Fluid–Structure Interaction by SPH
,”
Comput. Struct.
,
85
(
11–14
), pp.
879
890
.
48.
Koshizuka
,
S.
,
Oka
,
Y.
, and
Tamako
,
H.
,
1995
, “
A Particle Method for Calculating Splashing of Incompressible Viscous Fluid
,”
International Conference on Mathematics and Computations, Reactor Physics, and Environmental Analyses
, Chiba, Japan, Aug. 1–5, pp.
1514
1521
.
49.
Walhorn
,
E.
,
Kolke
,
A.
,
Hubner
,
B.
, and
Dinkler
,
D.
,
2005
, “
Coupling Within a Monolithic Model Involving Free Surface Flows
,”
Comput. Struct.
,
83
(
25–26
), pp.
2100
2111
.
50.
Marti
,
J.
,
Idelsohn
,
S.
,
Limache
,
A.
,
Calvo
,
N.
, and
D'Elia
,
J.
,
2006
, “
A Fully Coupled Particle Method for Quasi-Incompressible Fluid-Hypoelastic Structure Interactions
,”
Mech. Comput.
,
XXV
(9), pp.
809
827
.https://cimec.org.ar/ojs/index.php/mc/article/view/537/511
51.
Idelsohn
,
S.
,
Marti
,
J.
,
Limache
,
A.
, and
Onate
,
E.
,
2008
, “
Unified Lagrangian Formulation for Elastic Solids and Incompressible Fluids: Application to Fluid Structure Interaction Problems Via the PFEM
,”
Comput. Methods Appl. Mech. Eng.
,
197
(
19–20
), pp.
1762
1776
.
52.
Rafiee
,
A.
, and
Thiagarajan
,
K.
,
2009
, “
An SPH Projection Method for Simulating Fluid-Hypoelastic Structure Interaction
,”
Comput. Methods Appl. Mech. Eng.
,
198
(33–36), pp.
2785
2795
.
53.
Newmark
,
N. M.
,
1959
, “
A Method of Computation for Structural Dynamics
,”
J. Eng. Mech. ASCE
,
85
(3), pp.
67
94
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