In the present work, we present an improved version of the direct-forcing immersed boundary (IB) method proposed in Wang and Zhang (2011, “An Immersed Boundary Method Based on Discrete Stream Function Formulation for Two- and Three-Dimensional Incompressible Flows,” J. Comput. Phys., 230(9), pp. 3479–3499). In order to obtain an accurate prediction of local surface force, measures have been taken to suppress the unphysical spatial oscillations in the Lagrangian forcing. A fluid-structure interaction (FSI) solver has been developed by using the improved IB method for the fluid and the finite difference method for the structure. Several flow problems are simulated to validate our method. The testing cases include flows over a stationary cylinder and a stationary flat plate, two-dimensional flow past an inextensible flexible filament, and three-dimensional flow past a flapping flag. The results obtained in the present work agree well with those from the literature.

References

References
1.
Peskin
,
C. S.
,
2003
, “
The Immersed Boundary Method
,”
Acta Numer.
,
11
, pp.
479
517
.10.1017/S0962492902000077
2.
Mittal
,
R.
, and
Iaccarino
,
G.
,
2005
, “
Immersed Boundary Methods
,”
Ann. Rev. Fluid Mech.
,
37
, pp.
239
261
.10.1146/annurev.fluid.37.061903.175743
3.
Balaras
,
E.
, and
Yang
,
J.
,
2005
, “
Nonboundary Conforming Methods for Large-Eddy Simulations of Biological Flows
,”
ASME J. Fluids Eng.
,
127
(
5
), pp.
851
857
.10.1115/1.1988346
4.
Zhang
,
N.
, and
Zheng
,
Z. C.
,
2007
, “
An Improved Direct-Forcing Immersed-Boundary Method for Finite Difference Applications
,”
J. Comput. Phys.
,
221
(
1
), pp.
250
268
.10.1016/j.jcp.2006.06.012
5.
Narasimhan
,
M.
,
Dong
,
H.
,
Mittal
,
R.
, and
Singh
,
S. N.
,
2005
, “
Optimal Yaw Regulation and Trajectory Control of Biorobotic AUV Using Mechanical Fins Based on CFD Parameterization
,”
ASME J. Fluids Eng.
,
128
(
4
), pp.
687
698
.10.1115/1.2201634
6.
Wang
,
S.
, and
Zhang
,
X.
,
2011
, “
An Immersed Boundary Method Based on Discrete Stream Function Formulation for Two- and Three-Dimensional Incompressible Flows
,”
J. Comput. Phys.
,
230
(
9
), pp.
3479
3499
.10.1016/j.jcp.2011.01.045
7.
Su
,
S. W.
,
Lai
,
M. C.
, and
Lin
,
C. A.
,
2007
, “
An Immersed Boundary Technique for Simulating Complex Flows With Rigid Boundary
,”
Comput. Fluids
,
36
(
2
), pp.
313
324
.10.1016/j.compfluid.2005.09.004
8.
Uhlmann
,
M.
,
2005
, “
An Immersed Boundary Method With Direct Forcing for the Simulation of Particulate Flows
,”
J. Comput. Phys.
,
209
(
2
), pp.
448
476
.10.1016/j.jcp.2005.03.017
9.
Zhu
,
L.
, and
Peskin
,
C. S.
,
2002
, “
Simulation of a Flapping Flexible Filament in a Flowing Soap Film by the Immersed Boundary Method
,”
J. Comput. Phys.
,
179
(
2
), pp.
452
468
.10.1006/jcph.2002.7066
10.
Connell
,
B. S. H.
, and
Yue
,
D. K. P.
,
2007
, “
Flapping Dynamics of a Flag in a Uniform Stream
,”
J. Fluid Mech.
,
581
, pp.
33
67
.10.1017/S0022112007005307
11.
Huang
,
W.-X.
,
Shin
,
S. J.
, and
Sung
,
H. J.
,
2007
, “
Simulation of Flexible Filaments in a Uniform Flow by the Immersed Boundary Method
,”
J. Comput. Phys.
,
226
(
2
), pp.
2206
2228
.10.1016/j.jcp.2007.07.002
12.
Huang
,
W. X.
, and
Sung
,
H. J.
,
2010
, “
Three-Dimensional Simulation of a Flapping Flag in a Uniform Flow
,”
J. Fluid Mech.
,
653
, pp.
301
336
.10.1017/S0022112010000248
13.
Tornberg
,
A.-K.
, and
Engquist
,
B.
,
2004
, “
Numerical Approximations of Singular Source Terms in Differential Equations
,”
J. Comput. Phys.
,
200
(
2
), pp.
462
488
.10.1016/j.jcp.2004.04.011
14.
Linnick
,
M. N.
, and
Fasel
,
H. F.
,
2005
, “
A High-Order Immersed Interface Method for Simulating Unsteady Incompressible Flows on Irregular Domains
,”
J. Comput. Phys.
,
204
(
1
), pp.
157
192
.10.1016/j.jcp.2004.09.017
15.
Taira
,
K.
, and
Colonius
,
T.
,
2007
, “
The Immersed Boundary Method: A Projection Approach
,”
J. Comput. Phys.
,
225
(
2
), pp.
2118
2137
.10.1016/j.jcp.2007.03.005
16.
Majumdar
,
S.
,
Iaccarino
,
G.
, and
Durbin
,
P.
,
2001
, “
RANS Solvers With Adaptive Structured Boundary Non-Conforming Grids
,” Annual Research Briefs, Center for Turbulence Research, Stanford University, pp.
353
466
.
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