Despite recent interests in complex fluid–structure interaction (FSI) problems, little work has been conducted to establish baseline multidisciplinary FSI modeling capabilities for research and commercial activities across computational platforms. The current work investigates the fluid modules of contemporary FSI methodologies by solving a purely fluid problem at low Reynolds numbers to improve understanding of the fluid dynamic capabilities of each solver. By incorporating both monolithic and partitioned solvers, a holistic comparison of computational accuracy and time-expense is presented between lattice-Boltzmann methods (LBM), coupled Lagrangian–Eulerian (CLE), and smoothed particle hydrodynamics (SPH). These explicit methodologies are assessed using the classical square lid-driven cavity for low Reynolds numbers (100–3200) and are validated against an implicit Navier–Stokes solution in addition to established literature. From an investigation of numerical error associated with grid resolution, the Navier–Stokes solution, LBM, and CLE were all relatively mesh independent. However, SPH displayed a significant dependence on grid resolution and required the greatest computational expense. Throughout the range of Reynolds numbers investigated, both LBM and CLE closely matched the Navier–Stokes solution and literature, with the average velocity profile error along the generated cavity centerlines at 1% and 4%, respectively, at Re = 3200. SPH did not provide accurate results whereby the average error for the centerline velocity profiles was 31% for Re = 3200, and the methodology was unable to represent vorticity in the cavity corners. Results indicate that while both LBM and CLE show promise for modeling complex fluid flows, commercial implementations of SPH demand further development.

References

References
1.
Song
,
Y.
, and
Bayandor
,
J.
,
2014
, “
Comprehensive Soft Impact Damage Methodology for Advanced High Bypass Ratio Turbofan Engines
,”
ASME
Paper No. FEDSM2014-22110.
2.
Gursul
,
I.
,
2004
, “
Vortex Flows on UAVs: Issues and Challenges
,”
Aeronaut. J.
,
108
(
1090
), pp.
597
610
.
3.
Karimi
,
A.
,
Navidbakhsh
,
M.
,
Razaghi
,
R.
, and
Haghpanahi
,
M.
,
2014
, “
A Computational Fluid-Structure Interaction Model for Plaque Vulnerability Assessment in Atherosclerotic Human Coronary Arteries
,”
J. Appl. Phys.
,
115
(
14
), p.
144702
.
4.
Degroote
,
J.
,
Bathe
,
K.-J.
, and
Vierendeels
,
J.
,
2009
, “
Performance of a New Partitioned Procedure Versus a Monolithic Procedure in Fluid–Structure Interaction
,”
Comput. Struct.
,
87
(
11–12
), pp.
793
801
.
5.
Thurber
,
A.
, and
Bayandor
,
J.
,
2015
, “
On the Fluidic Response of Structures in Hypervelocity Impacts
,”
ASME J. Fluids Eng.
,
137
(
4
), p.
041101
.
6.
Song
,
Y.
, and
Bayandor
,
J.
,
2015
, “
Novel Implementation of Fluid-Solid Interaction Analysis in Air Breathing Propulsion Systems
,”
ASME
Paper No. AJKFluids2015-13347.
7.
Song
,
Y.
, and
Bayandor
,
J.
,
2016
, “
Analysis of Progressive Dynamic Damage Caused by Large Hailstone Ingestion Into Modern High Bypass Turbofan Engine
,”
AIAA
Paper No. 2016-0705.
8.
Heimbs
,
S.
,
2011
, “
Computational Methods for Bird Strike Simulations: A Review
,”
Comput. Struct.
,
89
(
23–24
), pp.
2093
2112
.
9.
Shao
,
J. R.
,
Li
,
H. Q.
,
Liu
,
G. R.
, and
Liu
,
M. B.
,
2012
, “
An Improved SPH Method for Modeling Liquid Sloshing Dynamics
,”
Comput. Struct.
,
100–101
(
3
), pp.
18
26
.
10.
Arumuga Perumal
,
D.
, and
Dass
,
A. K.
,
2011
, “
Multiplicity of Steady Solutions in Two-Dimensional Lid-Driven Cavity Flows by Lattice Boltzmann Method
,”
Comput. Math. Appl.
,
61
(
12
), pp.
3711
3721
.
11.
Chen
,
S.
, and
Doolen
,
G. D.
,
1998
, “
Lattice Boltzmann Method for Fluid Flows
,”
Annu. Rev. Fluid Mech.
,
30
(
1
), pp.
329
364
.
12.
Wood
,
S. L.
, and
Deiterding
,
R.
,
2015
, “
A Dynamically Adaptive Lattice Boltzmann Method for Flapping Wing Aerodynamics
,”
ASME
Paper No. AJKFluids2015-13802.
13.
Kollmannsberger
,
S.
,
Geller
,
S.
,
Düster
,
A.
,
Tölke
,
J.
,
Sorger
,
C.
,
Krafczyk
,
M.
, and
Rank
,
E.
,
2009
, “
Fixed-Grid Fluid-Structure Interaction in Two Dimensions Based on a Partitioned Lattice Boltzmann and p-FEM Approach
,”
Int. J. Numer. Methods Eng.
,
79
(
7
), pp.
817
845
.
14.
Ghia
,
U.
,
Ghia
,
K. N.
, and
Shin
,
C. T.
,
1982
, “
High-Re Solutions for Incompressible Flow Using the Navier–Stokes Equations and a Multigrid Method
,”
J. Comput. Phys.
,
48
(
3
), pp.
387
411
.
15.
Koseff
,
J. R.
, and
Street
,
R. L.
,
1984
, “
The Lid-Driven Cavity Flow: A Synthesis of Qualitative and Quantitative Observations
,”
ASME J. Fluids Eng.
,
106
(
12
), pp.
390
398
.
16.
Daggupati
,
S.
,
Mandapati
,
R. N.
,
Mahajani
,
S. M.
,
Ganesh
,
A.
,
Pal
,
A. K.
,
Sharma
,
R. K.
, and
Aghalayam
,
P.
,
2011
, “
Compartment Modeling for Flow Characterization of Underground Coal Gasification Cavity
,”
Ind. Eng. Chem. Res.
,
50
(
1
), pp.
277
290
.
17.
Bourgin
,
P.
, and
Saintlos
,
S.
,
2001
, “
High-Velocity Coating Flows and Other Related Problems
,”
Int. J. Non-Linear. Mech.
,
36
(
4
), pp.
585
596
.
18.
Burggraf
,
O. R.
,
1966
, “
Analytical and Numerical Studies of the Structure of Steady Separated Flows
,”
J. Fluid Mech.
,
24
(
1
), pp.
113
151
.
19.
Prasad
,
A. K.
, and
Koseff
,
J. R.
,
1989
, “
Reynolds Number and End-Wall Effects on a Lid-Driven Cavity Flow
,”
Phys. Fluids A
,
1
(
2
), pp.
208
218
.
20.
Hou
,
G.
,
Wang
,
J.
, and
Layton
,
A.
,
2012
, “
Numerical Methods for Fluid-Structure Interaction—A Review
,”
Commun. Comput. Phys.
,
12
(
2
), pp.
337
377
.
21.
Peng
,
Y. F.
,
Shiau
,
Y. H.
, and
Hwang
,
R. R.
,
2003
, “
Transition in a 2D Lid-Driven Cavity Flow
,”
Comput. Fluids
,
32
(
3
), pp.
337
352
.
22.
Perumal
,
D. A.
, and
Dass
,
A. K.
,
2013
, “
Application of Lattice Boltzmann Method for Incompressible Viscous Flows
,”
Appl. Math. Model.
,
37
(
6
), pp.
4075
4092
.
23.
Rafiee
,
A.
,
2008
, “
Modelling of Generalized Newtonian Lid-Driven Cavity Flow Using an SPH Method
,”
ANZIAM J.
,
49
(
3
), pp.
411
422
.
24.
Basa
,
M.
,
Quinlan
,
N. J.
, and
Lastiwka
,
M.
,
2009
, “
Robustness and Accuracy of SPH Formulations for Viscous Flow
,”
Int. J. Numer. Methods Fluids
,
60
(
10
), pp.
1127
1148
.
25.
Al-Amiri
,
A.
, and
Khanafer
,
K.
,
2011
, “
Fluid–Structure Interaction Analysis of Mixed Convection Heat Transfer in a Lid-Driven Cavity With a Flexible Bottom Wall
,”
Int. J. Heat Mass Transfer
,
54
(
17–18
), pp.
3826
3836
.
26.
Shapiro
,
A. H.
,
1953
,
The Dynamics and Thermodynamics of Compressible Fluid Flow
, Vol.
2
,
Ronald Press
,
New York
.
27.
Munson
,
B.
,
Young
,
D.
,
Okiishi
,
T.
, and
Huebasch
,
W.
,
2009
,
Fundamentals of Fluid Mechanics
,
Wiley
,
Hoboken, NJ
.
28.
ANSYS
,
2013
, “
Fluent 13.0 Theory Guide
,” ANSYS, Lebanon, NH.
29.
Kadanoff
,
L.
,
1986
, “
On Two Levels
,”
Phys. Today
,
39
(
9
), pp.
7
9
.
30.
Deiterding
,
R.
, and
Wood
,
S. L.
,
2016
, “
An Adaptive Lattice Boltzmann Method for Predicting Wake Fields Behind Wind Turbines
,”
New Results in Numerical and Experimental Fluid Mechanics X
(Notes on Numerical Fluid Mechanics and Multidisciplinary Design), Vol.
132
,
Springer
,
Cham, Switzerland
, pp.
845
857
.
31.
Sone
,
Y.
,
2007
,
Molecular Gas Dynamics: Theory, Techniques, and Applications
,
Birkhäuser
,
Basel, Switzerland
.
32.
Donea
,
J.
,
Giuliani
,
S.
, and
Halleux
,
J. P.
,
1982
, “
An Arbitrary Lagrangian-Eulerian Finite Element Method for Transient Dynamic Fluid-Structure Interaction
,”
Comput. Methods Appl. Mech. Eng.
,
33
(
1–3
), pp.
689
723
.
33.
Hallquist
,
J. O.
,
2015
, “
LS-DYNA Theory Manual
,” Livermore Software Technology Corp., Livermore, CA.
34.
Noh
,
W. F.
,
1963
, “
CEL: A Time-Dependent, Two-Space-Dimensional, Coupled Eulerian-Lagrange Code
,” Lawrence Radiation Laboratory, University of California, Livermore, CA, Report No.
UCRL-7463
.https://www.osti.gov/scitech/biblio/4621975-cel-time-dependent-two-space-dimensional-coupled-eulerian-lagrange-code
35.
Trulio
,
J. G.
,
1966
, “
Theory and Structure of the AFTON Codes
,” Air Force Weapons Laboratory, Kirtland Air Force Base, Newbury Park, CA, Report No.
AFWL-TR-66-19
.http://www.dtic.mil/dtic/tr/fulltext/u2/485510.pdf
36.
Braess
,
H.
, and
Wriggers
,
P.
,
2000
, “
Arbitrary Lagrangian Eulerian Finite Element Analysis of Free Surface Flow
,”
Comput. Methods Appl. Mech. Eng.
,
190
(
1–2
), pp.
95
109
.
37.
Van Leer
,
B.
,
1977
, “
Towards the Ultimate Conservative Difference Scheme—IV: A New Approach to Numerical Convection
,”
J. Comput. Phys.
,
23
(
3
), pp.
276
299
.
38.
Dukowicz
,
J. K.
, and
Kodis
,
J. W.
,
1987
, “
Accurate Conservative Remapping (Rezoning) for Arbitrary Lagrangian-Eulerian Computations
,”
SIAM J. Sci. Stat. Comput.
,
8
(
3
), pp.
305
321
.
39.
Lucy
,
L. B.
,
1977
, “
A Numerical Approach to the Testing of the Fission Hypothesis
,”
Astronaut. J.
,
82
(
12
), pp.
1013
1024
.
40.
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
.
41.
Li
,
S.
, and
Liu
,
W. K.
,
2002
, “
Meshfree and Particle Methods and Their Applications
,”
ASME Appl. Mech. Rev.
,
55
(
1
), pp.
1
34
.
42.
Gómez-Gesteira
,
M.
, and
Dalrymple
,
R. A.
,
2004
, “
Using a Three-Dimensional Smoothed Particle Hydrodynamics Method for Wave Impact on a Tall Structure
,”
J. Waterw. Port Coastal Ocean Eng.
,
130
(
2
), pp.
63
69
.
43.
Liu
,
G. R.
, and
Liu
,
M. B.
,
2000
,
Smoothed Particle Hydrodynamics
(A Meshfree Particle Method),
World Scientific
,
Singapore
.
44.
Monaghan
,
J.
,
1992
, “
Smoothed Particle Hydrodynamics
,”
Annu. Rev. Astron. Astrophys
,
30
(
1
), pp.
543
574
.
45.
Monaghan
,
J. J.
,
1985
, “
Particle Methods for Hydrodynamics
,”
Comput. Phys. Rep.
,
3
(
2
), pp.
71
124
.
46.
Benz
,
W.
,
1990
, “
Smooth Particle Hydrodynamics: A Review
,”
NATO Advanced Research Workshop on the Numerical Modelling of Nonlinear Stellar Pulsations Problems and Prospects
(
NMNS
), Les Arcs, France, Mar. 20–24, pp.
269
288
.http://adsabs.harvard.edu/abs/1990nmns.work..269B
47.
Anderson
,
J. D.
, and
Wendt
,
J.
,
1995
,
Computational Fluid Dynamics
,
Springer
,
Berlin
.
48.
Chen
,
J.-S.
,
Hu
,
W.
, and
Hu
,
H.-Y.
,
2009
, “
Localized Radial Basis Functions With Partition of Unity Properties
,”
Progress on Meshless Methods
,
Springer
,
Dordrecht, The Netherlands
, pp. 37–56.
49.
Vignjevic
,
R.
, and
Campbell
,
J.
,
2009
, “
Review of Development of the Smooth Particle Hydrodynamics
,”
Predictive Modeling of Dynamic Processes
,
Springer
,
Boston, MA
, pp.
367
396
.
50.
Roache
,
P. J.
,
1994
, “
Perspective: A Method for Uniform Reporting of Grid Refinement Studies
,”
ASME J. Fluids Eng.
,
116
(
3
), pp.
405
413
.
51.
Celik
,
I. B.
,
Ghia
,
U.
,
Roache
,
P. J.
,
Freitas
,
C. J.
,
Coleman
,
H.
, and
Raad
,
P. E.
,
2008
, “
Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications
,”
ASME J. Fluids Eng.
,
130
(
7
), p.
078001
.
52.
Roy
,
C. J.
,
2003
, “
Grid Convergence Error Analysis for Mixed-Order Numerical Schemes
,”
AIAA J.
,
41
(
4
), pp.
595
604
.
53.
Di Mascio
,
A.
,
Paciorri
,
R.
, and
Favini
,
B.
,
2002
, “
Truncation Error Analysis in Turbulent Boundary Layers
,”
ASME J. Fluids Eng.
,
124
(
3
), pp.
657
663
.
54.
Chiang
,
T. P.
,
Hwang
,
R. R.
, and
Sheu
,
W. H.
,
1997
, “
On End-Wall Corner Vortices in a Lid-Driven Cavity
,”
ASME J. Fluids Eng.
,
119
(
1
), pp.
201
203
.
55.
Shankar
,
P. N.
, and
Deshpande
,
M. D.
,
2000
, “
Fluid Mechanics in the Driven Cavity
,”
Annu. Rev. Fluid Mech.
,
32
(
1
), pp.
93
136
.
56.
Kawai
,
H.
,
Yasumasa
,
K.
, and
Tanahashi
,
T.
,
1989
, “
Numerical Flow Analysis in a Cubic Cavity by the GSMAC Finite Element Method: In the Case That Reynolds Numbers Are 1000 and 3200
,”
Trans. Jpn. Soc. Mech. Eng. Ser. B
,
33
(
4
), pp.
649
658
.
57.
Lee
,
E.-S.
,
Moulinec
,
C.
,
Xu
,
R.
,
Violeau
,
D.
,
Laurence
,
D.
, and
Stansby
,
P.
,
2008
, “
Comparisons of Weakly Compressible and Truly Incompressible Algorithms for the SPH Mesh Free Particle Method
,”
J. Comput. Phys.
,
227
(
18
), pp.
8417
8436
.
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