Accurately capturing boundaries is crucial for simulating fluid–structure interaction (FSI) problems involving flexible objects undergoing large deformations. This paper presents a coupling of the immersed boundary-lattice Boltzmann method with a node-based partly smoothed point interpolation method (NPS-PIM) to enhance the accuracy of simulating moving flexible bodies in FSI problems. The proposed method integrates a multiple relaxation time scheme and employs a force correction technique to address boundary capturing inaccuracies. The effect of virtual fluid is accounted for through a Lagrangian point approximation, ensuring precise FSI force calculations for unsteady solid motions. NPS-PIM is utilized as the solid solver, constructing a moderately softened model stiffness by combining the finite element method (FEM) with the node-based smoothed PIM (NS-PIM). Simulations of flow fields near flexible objects with large deformations demonstrate that the proposed approach reduces numerical errors, improves computational efficiency compared to traditional FSI models using FEM and NS-PIM, and accurately captures the behavior of moving flexible bodies and detailed flow fields.
REFERENCES
1.
R.
Mittal
and
G.
Iaccarino
, “
Immersed boundary methods
,” Annu. Rev. Fluid Mech.
37
, 239
–261
(2005
).2.
C. S.
Peskin
, “
Flow patterns around heart valves: A numerical method
,” J. Comput. Phys.
10
(2
), 252
–271
(1972
).3.
T. Y.
Hou
and
Z.
Shi
, “
Removing the stiffness of elastic force from the immersed boundary method for the 2D Stokes equations
,” J. Comput. Phys.
227
(21
), 9138
–9169
(2008
).4.
T. Y.
Hou
and
Z.
Shi
, “
An efficient semi-implicit immersed boundary method for the Navier–Stokes equations
,” J. Comput. Phys.
227
(20
), 8968
–8991
(2008
).5.
J.
Mohd-Yusof
, “
Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries
,” Cent. Turbul. Res. Annu. Res. Briefs
161
(1
), 317
–327
(1997
).6.
D.
Hui
,
Z.
Wang
,
Y.
Cai
,
W.
Wu
,
G.
Zhang
, and
M.
Liu
, “
An immersed boundary-lattice Boltzmann method with hybrid multiple relaxation times for viscoplastic fluid-structure interaction problems
,” Appl. Ocean Res.
119
, 103023
(2022
).7.
D.
Hui
,
Z.
Xu
,
W.
Wu
,
G.
Zhang
,
Q.
Wu
, and
M.
Liu
, “
Drafting, kissing, and tumbling of a pair of particles settling in non-Newtonian fluids
,” Phys. Fluids
34
(2
), 023301
(2022
).8.
G.-Q.
Chen
,
X.
Huang
,
A. M.
Zhang
,
S. P.
Wang
, and
T.
Li
, “
Three-dimensional simulation of a rising bubble in the presence of spherical obstacles by the immersed boundary–lattice Boltzmann method
,” Phys. Fluids
31
(9
), 097104
(2019
).9.
Y.
Xiao
,
G.
Zhang
,
D.
Hui
,
H.
Yan
,
S.
Feng
, and
S.
Wang
, “
Numerical simulation for water entry and exit of rigid bodies based on the immersed boundary-lattice Boltzmann method
,” J. Fluids Struct.
109
, 103486
(2022
).10.
Y.
Cai
,
J.
Lu
, and
S.
Li
, “
Direct simulation of acoustic scattering problems involving fluid-structure interaction using an efficient immersed boundary-lattice Boltzmann method
,” J. Acoust. Soc. Am.
144
(4
), 2256
–2268
(2018
).11.
Y.
Cai
,
S.
Wang
,
J.
Lu
,
S.
Li
, and
G.
Zhang
, “
Efficient immersed-boundary lattice Boltzmann scheme for fluid-structure interaction problems involving large solid deformation
,” Phys. Rev. E
99
(2
), 023310
(2019
).12.
J.
Wu
and
C.
Shu
, “
Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications
,” J. Comput. Phys.
228
(6
), 1963
–1979
(2009
).13.
T.
Seta
,
R.
Rojas
,
K.
Hayashi
, and
A.
Tomiyama
, “
Implicit-correction-based immersed boundary–lattice Boltzmann method with two relaxation times
,” Phys. Rev. E
89
(2
), 023307
(2014
).14.
Z.
Chen
,
C.
Shu
,
D.
Tan
, and
C.
Wu
, “
On improvements of simplified and highly stable lattice Boltzmann method: Formulations, boundary treatment, and stability analysis
,” Numer. Methods Fluids
87
(4
), 161
–179
(2018
).15.
Y.
Cai
,
S.
Li
, and
J.
Lu
, “
An improved immersed boundary‐lattice Boltzmann method based on force correction technique
,” Numer. Methods Fluids
87
(3
), 109
–133
(2018
).16.
L.
Shen
,
E.
Chan
, and
P.
Lin
, “
Calculation of hydrodynamic forces acting on a submerged moving object using immersed boundary method
,” Comput. Fluids
38
(3
), 691
–702
(2009
).17.
Y.
Cai
,
J.
Lu
,
S.
Wang
,
Y.
Xia
, and
S.
Li
, “
A Lagrangian point approximation-based immersed boundary–lattice Boltzmann method for FSI problems involving deformable body
,” Int. J. Comput. Methods
19
(3
), 2150070
(2022
).18.
W.
Li
,
W. Q.
Wang
,
Y.
Yan
, and
Z. F.
Yu
, “
A strong-coupled method combined finite element method and lattice Boltzmann method via an implicit immersed boundary scheme for fluid structure interaction
,” Ocean Eng.
214
, 107779
(2020
).19.
Z.
Li
,
G.
Oger
, and
D.
Le Touzé
, “
A partitioned framework for coupling LBM and FEM through an implicit IBM allowing non-conforming time-steps: Application to fluid-structure interaction in biomechanics
,” J. Comput. Phys.
449
, 110786
(2022
).20.
J.
Qin
,
Y.
Andreopoulos
,
X.
Jiang
,
G.
Dong
, and
Z.
Chen
, “
Efficient coupling of direct forcing immersed boundary‐lattice Boltzmann method and finite element method to simulate fluid‐structure interactions
,” Numer. Methods Fluids
92
(6
), 545
–572
(2020
).21.
A.
Khoshghalb
,
A.
Shafee
,
A.
Tootoonchi
,
O.
Ghaffaripour
, and
S.
Jazaeri
, “
Application of the smoothed point interpolation methods in computational geomechanics: A comparative study
,” Comput. Geotech.
126
, 103714
(2020
).22.
G.
Zhang
,
Z.
Chen
,
Z.
Sui
,
D.
Tao
,
Z.
He
,
Q.
Tang
et al, “
A cell‐based smoothed radial point interpolation method with virtual nodes for three‐dimensional mid‐frequency acoustic problems
,” Numer. Methods Eng.
119
(6
), 548
–566
(2019
).23.
G.
Zhang
,
H.
Lu
,
D.
Yu
,
Z.
Bao
, and
H.
Wang
, “
A node-based partly smoothed point interpolation method (NPS-PIM) for dynamic analysis of solids
,” Eng. Anal. Boundary Elem.
87
, 165
–172
(2018
).24.
G.
Zhang
,
S.
Wang
,
Z.
Sui
,
L.
Sun
,
Z.
Zhang
, and
Z.
Zong
, “
Coupling of SPH with smoothed point interpolation method for violent fluid-structure interaction problems
,” Eng. Anal. Boundary Elem.
103
, 1
–10
(2019
).25.
S.
Wang
,
Y.
Cai
,
G.
Zhang
,
X.
Quan
,
J.
Lu
, and
S.
Li
, “
A coupled immersed boundary‐lattice Boltzmann method with smoothed point interpolation method for fluid‐structure interaction problems
,” Numer. Methods Fluids
88
(8
), 363
–384
(2018
).26.
S.
Wang
,
G.
Zhang
,
Z.
Zhang
,
D.
Hui
, and
Z.
Zong
, “
An immersed smoothed point interpolation method (IS‐PIM) for fluid‐structure interaction problems
,” Numer. Methods Fluids
85
(4
), 213
–234
(2017
).27.
J.
Lu
,
H.
Han
,
B.
Shi
, and
Z.
Guo
, “
Immersed boundary lattice Boltzmann model based on multiple relaxation times
,” Phys. Rev. E
85
(1
), 016711
(2012
).28.
Y. H.
Qian
, “
Lattice BGK models for Navier-Stokes equation
,” Europhys. Lett.
17
(6
), 479
–484
(1992
).29.
X.
He
and
L. S.
Luo
, “
Lattice Boltzmann model for the incompressible Navier–Stokes equation
,” J. Stat. Phys.
88
(3
), 927
–944
(1997
).30.
I.
Ginzbourg
and
P.
Adler
, “
Boundary flow condition analysis for the three-dimensional lattice Boltzmann model
,” J. Phys. II France
4
(2
), 191
–214
(1994
).31.
S. K.
Kang
and
Y. A.
Hassan
, “
A comparative study of direct-forcing immersed boundary-lattice Boltzmann methods for stationary complex boundaries
,” Numer. Methods Fluids
66
(9
), 1132
–1158
(2011
).32.
C. S.
Peskin
, “
The immersed boundary method
,” Acta Numer.
11
, 479
–517
(2002
).33.
J.
Kim
,
D.
Kim
, and
H.
Choi
, “
An immersed-boundary finite-volume method for simulations of flow in complex geometries
,” J. Comput. Phys.
171
(1
), 132
–150
(2001
).34.
M.-C.
Lai
and
C. S.
Peskin
, “
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
,” J. Comput. Phys.
160
(2
), 705
–719
(2000
).35.
T.
Belytschko
,
W. K.
Liu
, and
B.
Moran
, Nonlinear Finite Elements for Continua and Structures
(
John Wiley & Sons
,
Chichester
, 2000
).36.
G. R.
Liu
and
Y. T.
Gu
, “
A point interpolation method for two-dimensional solids
,” Int. J. Numer. Methods Eng.
50
(4
), 937
–951
(2001
).37.
J. G.
Wang
and
G. R.
Liu
, “
A point interpolation meshless method based on radial basis functions
,” Numer. Methods Eng.
54
(11
), 1623
–1648
(2002
).38.
G. R.
Liu
and
G. Y.
Zhang
, Smoothed Point Interpolation Methods: G Space Theory and Weakened Weak Forms
(
World Scientific Press
,
Singapore
, 2013
).39.
G. R.
Liu
, Meshfree Methods: Moving beyond the Finite Element Method
, 2nd ed. (
CRC Press
,
Boca Taton, FL
, 2009
).40.
Z.
Zhang
,
G.
Liu
, and
B. C.
Khoo
, “
Immersed smoothed finite element method for two dimensional fluid–structure interaction problems
,” Numer. Methods Eng.
90
(10
), 1292
–1320
(2012
).41.
S.
Wang
,
G.
Zhang
,
Y.
Cai
et al, “
Comparisons of two representative methods classified as immersed boundary and domain methods
,” Eng. Anal. Boundary Elem.
132
, 383
–398
(2021
).42.
S.
Wang
,
G.
Zhang
,
B.
Yan
et al, “
Simulating fluid-structure interactions with a hybrid immersed smoothed point interpolation method
,” Eng. Anal. Boundary Elem.
130
, 352
–363
(2021
).43.
S.
Turek
and
J.
Hron
, “
Proposal for numerical benchmarking of fluid–structure interaction between an elastic object and laminar incompressible flow
,” in Fluid–Structure Interaction (Lecture Notes in Computational Science and Engineering)
, edited by
H. J.
Bungartz
and
M.
Schäfer
(
Springer
,
Berlin, Heidelberg
, 2006
), pp. 371
–85
.44.
I. B.
Celik
,
U.
Ghia
,
P. J.
Roache
,
C. J.
Freitas
,
H.
Coleman
, and
P. E.
Raad
, “
Procedure for estimation and reporting of uncertainty due to discretization in CFD applications
,” J. Fluids Eng.
130
, 078001
(2008
).45.
S.
Turek
,
J.
Hron
,
M.
Madlik
,
M.
Razzaq
,
H.
Wobker
, and
J. F.
Acker
, “
Numerical simulation and benchmarking of a monolithic multigrid solver for fluid-structure interaction problems with application to hemodynamics
,” in Fluid Structure Interaction II
(
Springer
, 2011
), pp. 193
–220
.46.
T.
Dunne
, “
An Eulerian approach to fluid–structure interaction and goal‐oriented mesh adaptation
,” Numer. Methods Fluids
51
(9
), 1017
–1039
(2006
).47.
W. X.
Huang
and
H. J.
Sung
, “
An immersed boundary method for fluid–flexible structure interaction
,” Comput. Methods Appl. Mech. Eng.
198
(33
), 2650
–2661
(2009
).48.
X.
Wang
and
L. T.
Zhang
, “
Interpolation functions in the immersed boundary and finite element methods
,” Comput. Mech.
45
(4
), 321
–334
(2010
).49.
Z. Q.
Zhang
,
G. R.
Liu
, and
B. C.
Khoo
, “
A three dimensional immersed smoothed finite element method (3D IS-FEM) for fluid–structure interaction problems
,” Comput. Mech.
51
(2
), 129
–150
(2013
).50.
K.
Sugiyama
,
S.
Ii
,
S.
Takeuchi
,
S.
Takagi
, and
Y.
Matsumoto
, “
A full Eulerian finite difference approach for solving fluid–structure coupling problems
,” J. Comput. Phys.
230
(3
), 596
–627
(2011
).51.
W. Q.
Wang
,
R.
Yin
,
D. W.
Hao
et al, “
Modeling and simulation of fish-like swimming in a straight-line swimming state using immersed boundary method
,” Adv. Mech. Eng.
6
, 489683
(2014
).52.
E. D.
Tytell
,
C. Y.
Hsu
,
T. L.
Williams
et al, “
Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming
,” Proc. Natl. Acad. Sci. U. S. A.
107
, 19832
–19837
(2010
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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