The application of the Immersed Boundary (IB) method to simulate incompressible, turbulent flows around complex configurations is illustrated; the IB is based on the use of non-body conformal grids, and the effect of the presence of a body in the flow is accounted for by modifying the governing equations. Turbulence is modeled using standard Reynolds-Averaged Navier-Stokes models or the more sophisticated Large Eddy Simulation approach. The main features of the IB technique are described with emphasis on the treatment of boundary conditions at an immersed surface. Examples of flows around a cylinder, in a wavy channel, inside a stirred tank and a piston/cylinder assembly, and around a road vehicle are presented. Comparison with experimental data shows the accuracy of the present technique. This review article cites 70 references.
Issue Section:
Review Articles
1.
Vieceli
JA
(1969
), A method for including arbitrary external boundaries in the MAC incompressible fluid computing technique
, J. Comput. Phys.
4
, 543
–551
.2.
Welch JE, Harlow FH, Shannon JP, and Daly BJ (1966), A computing technique for solving viscous incompressible transient fluid flow problems involving free-surfaces, Report LA-3425, Los Alamos Scientific Lab.
3.
Harlow
FH
and Welch
JE
(1965
), Numerical calculation of time-dependent viscous incompressible flows of fluid with free surface
, Phys. Fluids
8
, 2182
2182
.4.
Vieceli
JA
(1971
), A computing method for incompressible flows bounded by moving walls
, J. Comput. Phys.
8
, 119
–143
.5.
Peskin CS (1972), Flow patterns around heart valves: A digital computer method for solving the equations of motion, PhD thesis, Physiology, Albert Einstein College of Medicine, Univ Microfilms 72–30, 378.
6.
Peskin
CS
(1977
), Numerical analysis of blood flow in the heart
, J. Comput. Phys.
25
, 220
–252
.7.
Peskin
CS
(1982
), The fluid dynamics of heart valves: Experimental, theoretical and computational methods
, Annu. Rev. Fluid Mech.
14
, 235
235
.8.
Peskin
CS
and McQueen
DM
(1989
), A three-dimensional computational method for blood flow in the heart: (I) immersed elastic fibers in a viscous incompressible fluid
, J. Comput. Phys.
81
, 372
–405
.9.
McQueen
DM
and Peskin
CS
(1989
), A three-dimensional computational method for blood flow in the heart: (II) contractile fibers
, J. Comput. Phys.
82
, 289
–297
.10.
Basdevant C and Sadourny R (1984), Numerical solution of incompressible flow: the mask method, Lab di Meteorologie Dynamique, Ecole Normale Superieure, Paris (unpublished).
11.
Briscolini
M
and Santangelo
P
(1989
), Development of the mask method for incompressible unsteady flows
, J. Comput. Phys.
84
, 57
–75
.12.
Goldstein
D
, Handler
R
, and Sirovich
L
(1993
), Modeling no-slip flow boundary with an external force field
, J. Comput. Phys.
105
, 354
–366
.13.
Saiki
EM
and Biringen
S
(1996
), Numerical simulation of a cylinder in uniform flow: Application of a virtual boundary method
, J. Comput. Phys.
123
, 450
450
.14.
LeVeque RJ and Calhoun D (1999), Cartesian grid methods for fluid flow in complex geometries, Computational Modeling in Biological Fluid Dynamics, LJ Fauci and S Gueron (eds) IMA Volumes in Mathematics and its Applications, 124, 117–143.
15.
Lai
MC
and Peskin
CS
(2000
), An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
, J. Comput. Phys.
160
, 705
–719
.16.
Mohd-Yosuf J (1997), Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries, Annual Research Briefs, Center for Turbulence Research, 317–328.
17.
Fadlun
EA
, Verzicco
R
, Orlandi
P
, and Mohd-Yusof
J
(2000
), Combined immersed-boundary/finite-difference methods for three-dimensional complex flow simulations
, J. Comput. Phys.
161
, 35
–60
.18.
Verzicco
R
, Mohd-Yusof
J
, Orlandi
P
, and Haworth
D
(2000
), LES in complex geometries using boundary body forces
, AIAA J.
38
, 427
–433
.19.
Khadra K, Parneix S, Angot P, and Caltagirone JP (1995), Fictitious domain approach for numerical modeling of Navier-Stokes equations, 4th Int Conf on Navier-Stokes Equations and Related Nonlinear Problem.
20.
Khadra
K
, Angot
P
, Parneix
S
, and Caltagirone
JP
(2000
), Fictitious domain approach for numerical modelling of Navier-Stokes equations
, Int. J. Numer. Methods Fluids
34
, 651
–684
.21.
Angot
P
, Bruneau
CH
, and Frabrie
P
(1999
), A penalization method to take into account obstacles in viscous flows
, Numerische Mathematik
81
, 497
–520
.22.
Kevlahan
N
and Ghidaglia
JM
(2001
), Computation of turbulent flow past an array of cylinders using a spectral method with Brinkman penalization
, Eur. J. Mech. B/Fluids
20
, 333
–350
.23.
Berger M and Aftosmis M (1998), Aspects (and aspect ratios) of Cartesian mesh methods, 16th Int Conf on Numerical Methods in Fluid Dynamics.
24.
Aftosmis MJ, Berger MJ, and Adomavicius G (2000), A parallel multilevel method for adaptively refined Cartesian grids with embedded boundaries, AIAA Paper 2000-0808.
25.
Forrer H (1997), Boundary treatments for Cartesian-grid methods, PhD thesis, Swiss Federal Inst of Tech.
26.
Ye
T
, Mittal
R
, Udaykumar
HS
, and Shyy
W
(1999
), An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
, J. Comput. Phys.
156
, 209
–240
.27.
Coirier WJ (1994), An adaptively-refined, Cartesian, cell-based scheme for the Euler and Navier-Stokes equations, NASA TM106754.
28.
Almgren
AS
, Bell
JB
, Colella
P
, and Marthaler
T
(1997
), A Cartesian grid projection method for the incompressible Euler equations in complex geometries
, SIAM J. Sci. Comput. (USA)
18
, 1289
–1309
.29.
Hirt
CW
and Nichols
BD
(1981
), Volume of fluid (VOF) method for the dynamics of free boundaries
, J. Comput. Phys.
, 39
, 201
–225
.30.
Sethian JA (1996), Level Set Methods and Fast Marching Methods, Cambridge Univ Press.
31.
Duchamp de Lageneste L and Pitsch H (2000), A level-set approach to large eddy simulation of premixed turbulent combustion, Ann Res Briefs-2000, Center for Turbulence Research, Stanford Univ, 105–116.
32.
Germano
M
, Piomelli
U
, Moin
P
, and Cabot
WH
(1991
), A dynamic subgrid-scale eddy viscosity model
, Phys. Fluids A
3
, 1760
–1765
.33.
Lilly
DK
(1992
), A proposed modification of the Germano subgrid-scale closure method
, Phys. Fluids A
4
, 633
–635
.34.
Smagorinsky
J
(1963
), General circulation experiments with primitive equations
, Mon. Weather Rev.
91
, 99
–164
.35.
Verzicco
R
and Orlandi
P
(1996
), A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates
, J. Comput. Phys.
123
, 402
402
.36.
Orlandi P (2000), Fluid Flow Phenomena: A Numerical Toolkit, Kluwer Acad Pub, 355.
37.
Jones
WP
, and Launder
BE
(1972
), The prediction of laminarization with a two-equation model of turbulence
, Int. J. Heat Mass Transf.
15
, 1
–32
.38.
Spalart
PR
and Allmaras
SR
(1994
), A one-equation turbulence model for aerodynamic flows
, La Recherche Aerospatiale
, 1
, 1
–23
.39.
Majumdar S, Iaccarino G, and Durbin PA (2001), RANS solver with adaptive structured boundary non-conforming grids, Annual Research Briefs 2001, Center For Turbulence Research, 353.
40.
Franke
R
(1982
), Scattered data interpolation: Tests of some methods
, Math. Comput.
38
, 181
–200
.41.
Tessicini F, Verzicco R, and Orlandi P (2001), Effetti della geometria dell’ugello sull’evoluzione di un getto libero, Atti del XV Congresso AIMETA, SP FL 20, 2001 (see also Nozzle geometry effects in the near field of a round jet, Jets in Cross Flow, CISM, Udine, (2001) Cortelezzi and Karagozian (eds) Springer–Verlag).
42.
O’Rourke J (1998), Computational Geometry in C, Cambridge University Press.
43.
Aftosmis MJ, Delanaye M, and Haimes R (1999), Automatic generation of CFD-ready surface triangulations from CAD geometry, AIAA Paper 99–0776.
44.
De Zeeuw
D
and Powell
KG
(1993
), An adaptive Cartesian mesh method for the Euler equations
, J. Comput. Phys.
104
, 5668
5668
.45.
Pember
RJ
, Bell
BJ
, Colella
P
, Crutchfield
WJ
, and Welcome
ML
(1995
), An adaptive Cartesian grid method for unsteady compressible flow in irregular regions
, J. Comput. Phys.
1120
, 278
–304
.46.
Ferziger JH and Peric M (1999), Computational Methods for Fluid Dynamics, Springer-Verlag.
47.
Durbin
PA
and Iaccarino
G
(2002
), An approach for local grid refinement of structured grids
, J. Comput. Phys.
181
, 639
–653
.48.
Williamson
CHK
(1996
), Vortex dynamics in the cylinder wake
, Annu. Rev. Fluid Mech.
28
, 477
477
.49.
Orlandi P, Leonardi S, Tessicini F and Verzicco R (2001), Scie tridimensionali generate da cilindri con e senza ondulazioni, Atti del XV Congresso AIMETA, SP FL 12, Taormina, Italy.
50.
Prasad
A
and Williamson
CHK
(1996
), The instability of separated shear layer from a bluff body
, Phys. Fluids
8
, 1347
1347
.51.
Lourenco L and Shih C 2000, Characteristics of the plane turbulent near wake of a circular cylinder: A particle image velocimetry study (Unpublished results taken from 53).
52.
Ong
L
and Wallace
J
(1996
), The velocity field of a turbulent very near wake of a circular cylinder
, Exp. Fluids
20
, 441
441
.53.
Kravchenko
A
and Moin
P
(2000
), Numerical studies of flow over a circular cylinder at ReD=3900,
Phys. Fluids
12
, 403
–417
.54.
Breuer M (1997), Numerical modeling influences on large eddy simulations for the flow past a circular cylinder, Proc of 11th Symp on Turbulent Shear Flows, Grenoble, France, 26:7–26:12.
55.
Tessicini F (2002), Large eddy simulation of the flow around a circular cylinder using an immersed boundary method, Paper in preparation, (personal communication).
56.
Leonardi S and Orlandi P (2001) DNS of turbulent flows in a channel with roughness, Proc of Dles4, Univ of Twente Enschede, Netherlands, 181–189.
57.
Kuzan JD (1986), Velocity measurements for turbulent separated and near-separated flows over solid waves, PhD thesis, Dept of Chem Eng, Univ of Illinois, Urbana IL.
58.
Rogers
S
and Kwak
D
(1990
), Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations
, AIAA J.
28
(2
), 253
–262
.59.
Morse AP, Whitelaw JH, and Yianneskis M (1978) Turbulent flow measurements by laser doppler anemometry in a motored reciprocating engine, Report FS/78/24, Imperial College, Dept of Mesh Eng.
60.
Haworth DC and Jansen K (1997), Large-eddy simulation on unstructured deforming meshes: Towards reciprocating IC engines, Comput. Fluids (submitted).
61.
Dong
L
, Johansen
ST
, and Engh
TA
(1994
), Flow induced by an impeller in an unbaffled tank-I. experimental
, Chem. Eng. Sci.
49
(4
), 549
549
.62.
Verzicco R, Iaccarino G, Fatica M, and Orlandi P (2000), Flow in an impeller stirred tank using an immersed boundary technique, Annual Research Briefs 2000, Center For Turbulence Research, 251 (submitted to AIChE J).
63.
Khalighi B, Zhang S, Koromilas C, Balkanyi SR, Bernal LP, Iaccarino G, and Moin P (2001), Experimental and computational study of unsteady wake flow behind a bluff body with a drag reduction device, SAE Paper, 2001-01B-207.
64.
Verzicco
R
, Fatica
M
, Iaccarino
G
, Moin
P
, and Khalighi
B
(2002
), Large eddy simulation of a road-vehicle with drag reduction devices
, AIAA J
40
(12
), 2447
–2455
.65.
Balaras E and Benocci C (1994), Subgrid-scale models in finite-difference simulations in complex wall bounded flows, AGARD CP 551, 2.1.
66.
Balaras
E
, Benocci
C
, and Piomelli
U
(1996
), Two-layer approximate boundary conditions for large-eddy simulations
, AIAA J.
34
, 1111
–1119
.67.
Cabot WH (1995), Large-eddy simulation with wall models, Ann Res Briefs-1995, Center for Turbulence Research, Stanford Univ, 41–50.
68.
Cabot
WH
, and Moin
P
(1999
), Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flows
, Flow, Turbul. Combust.
63
, 269
–291
.69.
Wang
M
and Moin
P
(2002
), Dynamic wall modeling for LES of complex turbulent flows
, Phys. Fluids.
14
(7
), 2043
–2051
.70.
Wang
M
, and Moin
P
(2000
), Computation of trailing-edge flow and noise using large-eddy simulation
, AIAA J.
38
, 2201
–2209
.Copyright © 2003
by ASME
You do not currently have access to this content.
