This paper is a personal recollection of the development of computational fluid dynamics (CFD) at Imperial College (IC) in the 1960s by a group founded by Brian Spalding who was the charismatic leader of a dedicated team for a decade. I was a member of this team during the development of the basic engineering practice that came to be known as the IC approach to “CFD.” I hope to capture the essence and the significance of those developments. A version of this paper was delivered at the occasion of the seminar organized at Villanova University to celebrate the award of the 2010 Franklin Prize to Prof. Spalding. In a very strict sense the IC group invented neither the art and science of CFD nor the name. However it did excel in adapting and developing the methodology and technology of CFD, testing and verifying it against empirical data, and developing innovative and practical computational tools that had widespread application and relevance to problems of interest to engineers. In a nutshell the IC group heralded the CFD revolution and was the pioneer of the practice and technology of CFD. Most of today's commercially available software tools trace their origin to the work done by the IC group in the decade spanning the mid-60s to mid-70s. The group at IC benefitted tremendously and borrowed liberally from the innovative and groundbreaking work being carried out around this time at Los Alamos National Laboratory under the leadership of Frank Harlow—this is described elsewhere in this volume.

References

1.
Spalding
,
D. B.
,
1951
, “
The Combustion of Liquid Fuels
,” Ph.D. thesis,
Cambridge University
, Cambridge, UK.
2.
Spalding
,
D. B.
,
1963
,
Convective Mass Transfer: An Introduction
,
Edward Arnold (Publishers) Ltd.
,
London
.
3.
von Karman
,
T.
,
1921
, “
Uber Laminare und Turbulente Reibung
,”
Z Angew. Math. Mech.
,
1
, pp.
233
252
.10.1002/zamm.19210010401
4.
Kruzhilin
,
G. N.
,
1936
, “
Issledovanie Teplovogo Pogranichnogo Sloia
,”
Zh. Tekh. Fiz.
,
2
, pp.
183
190
.
5.
Eckert
,
E. R. G.
, and
Lieblein
,
V.
,
1949
, “
Berechnung Des Stoffüberganges an Einer Ebenen, Längs Angeströmten Oberfläche Bei Großem Teildruckgefälle
,”
Forsch. Geb. Ingenieurwes.
,
16
(
2
), pp.
33
42
.10.1007/BF02592487
6.
Spalding
,
D. B.
,
1964
, “
A Unified Theory of Friction, Heat Transfer, and Mass Transfer in the Turbulent Boundary Layer and Wall Jet
,” Her Majesty's Stationery Office, London, March, UK Aeronautical Research Council Report No. A.R.C. 25 925.
7.
Ricou
,
F. P.
, and
Spalding
,
D. B.
,
1961
, “
Measurements of Entrainment by Axisymmetrical Turbulent Jets
,”
J. Fluid Mech.
,
11
(
1
), pp.
21
32
.10.1017/S0022112061000834
8.
Escudier
,
M. P.
, and
Nicoll
,
W. B.
,
1966
, “
The Entrainment Function in Turbulent-Boundary-Layer and Wall-Jet Calculations
,”
J. Fluid Mech.
,
25
, pp.
337
366
.10.1017/S0022112066001691
9.
Escudier
,
M. P.
,
1967
, “
The Turbulent Incompressible Hydrodynamic Boundary Layer
,” Ph.D. thesis,
Imperial College, London University
,
UK
.
10.
Jayatilleke
,
C. L. V.
,
1969
, “
The Influence of Prandtl Number and Surface Roughness on the Resistance of the Laminar Sub-Layer to Momentum and Heat Transfer
,”
Prog. Heat Mass Transfer
,
1
, pp.
193
329
.
11.
Harlow
,
F. H.
,
2004
, “
Fluid Dynamics in Group T-3
,”
J. Comput. Phys.
,
195
, pp.
414
433
.10.1016/j.jcp.2003.09.031
12.
Runchal
,
A. K.
,
2009
, “
Brian Spalding: CFD and Reality—A Personal Recollection
,”
Int. J. Heat Mass Transfer
,
52
, pp.
4063
4073
.10.1016/j.ijheatmasstransfer.2009.03.058
13.
Artemov
,
V.
,
Escudier
,
M. P.
,
Fueyo
,
N.
,
Launder
,
B. E.
,
Leonardi
,
E.
,
Malin
,
M. R.
,
Minkowycz
,
W. J.
,
Patankar
,
S. V.
,
Pollard
,
A.
,
Rodi
,
W.
,
Runchal
,
A.
, and
Vanka
,
S. P.
,
2009
, “
A Tribute to D.B. Spalding and His Contributions in Science and Engineering
,”
Int. J. Heat Mass Transfer
,
52
, pp.
3884
3905
.10.1016/j.ijheatmasstransfer.2009.03.038
14.
Pohlhausen
,
K.
,
1921
, “
Zur Näherungsweisen Integration der Differentialgleichung der Laminaren Grenzschicht
,”
ZAMM I
, pp.
252
208
.10.1002/zamm.19210010402
15.
Morton
,
B. R.
,
Taylor
,
G. I.
, and
Turner
,
J. S.
,
1956
,
“Turbulent Gravitational Convection From Maintained and Instantaneous Sources
,”
Proc. R. Soc. London A
,
234
, pp.
1
23
.10.1098/rspa.1956.0011
16.
Patankar
,
S. V.
, and
Spalding
,
D. B.
,
1966
, “
A Calculation Procedure for Heat Transfer by Forced Convection Through Two-Dimensional Uniform-Property Turbulent Boundary Layers on Smooth Impermeable Walls
,”
Proceedings 3rd International Heat Transfer Conference
,
Chicago
,
Vol. 2
,
pp. 50–6
3
.
17.
Patankar
,
S. V.
, and
Spalding
,
D. B.
,
1967
,
Heat and Mass Transfer in Boundary Layers
,
Morgan-Grampian
,
London
.
18.
Patankar
,
S. V.
, and
Spalding
,
D. B.
,
1970
,
Heat and Mass Transfer in Boundary Layers: A General Calculation Procedure
, 2nd ed.,
Intertext Books
,
London
.
19.
Spalding
,
D. B.
,
1977
,
GENMIX: A General Computer Program for Two-Dimensional Parabolic Phenomena
, 1st ed.,
Pergamon Press
,
Oxford
.
20.
Runchal
,
A. K.
,
1972
, “
Convergence and Accuracy of Three Finite–Difference Schemes for a Two-Dimensional Conduction and Convection Problem
,”
Int. J. Numer. Methods Eng.
,
4
, pp.
540
550
.10.1002/nme.1620040408
21.
Spalding
,
D. B.
,
1981
, “
A General Purpose Computer Program for Multi-Dimensional One- and Two-Phase Flow
,”
Math. Comput. Simul.
,
23
, pp.
267
276
.10.1016/0378-4754(81)90083-5
22.
Thom
,
A.
,
1928
, “
An Investigation of Fluid Flow in Two Dimensions
,”
Aerospace Research Council
,
United Kingdom
, R & M No. 1194.
23.
Southwell
,
R. V.
,
1946
,
Relaxation Methods in Theoretical Physics
,
Oxford University Press
,
New York
.
24.
von Neumann
,
J.
,
1944
, “
Proposal for Analysis of Numerical Method for the Treatment of Hydrodynamical Shock Problems
,”
National Defense and Research Committee
, Report No. AM-551, March.
25.
Courant
,
R.
,
Isaacson
E.
, and
Rees
,
M.
,
1952
, “
On the Solution of Non-Linear Hyperbolic Differential Equations by Finite-Differences
,”
Commun. Pure Appl. Math.
,
5
, pp.
243
255
.10.1002/cpa.3160050303
26.
Burggraf
,
O. R.
,
1966
, “
Analytical and Numerical Studies of Steady Separated Flows
,”
J. Fluid Mech.
,
24
, pp.
113
151
.10.1017/S0022112066000545
27.
Runchal
,
A. K.
, and
Wolfshtein
,
M.
,
1966
, “
A Finite-Difference Procedure for the Integration of the Navier-Stokes Equations
,”
Imperial College, Mechanical Engineering Department, Report No. SF/TN/1
.
28.
Runchal
,
A. K.
,
Spalding
,
D. B.
, and
Wolfshtein
,
M.
,
1967
, “
The Numerical Solution of the Elliptic Equations for the Transport of Vorticity, Heat and Matter in Two Dimensional Flows
,”
Imperial College, Mechanical Engineering Department, Report No. SF/TN/2
.
29.
Runchal
,
A. K.
, and
Wolfshtein
,
M.
,
1967
, “
A Fortran IV Computer Program for the Solution of Steady-State, Two-Dimensional Equations of Motion, Energy and Concentrations
,”
Imperial College, Mechanical Engineering Department, Report No. SF/TN/10
.
30.
Runchal
,
A. K.
,
1967
, “
Three Finite-Difference Methods for Navier-Stokes Equations
,”
Proceedings of 2nd Applied Mechanics Conference
,
University of Strathclyde
,
Glasgow
.
31.
Runchal
,
A. K.
, and
Wolfshtein
,
M.
,
1969
, “
Numerical Integration Procedure for the Steady-State Navier-Stokes Equations
,”
J. Mech. Eng. Sci.
,
5
, pp.
445
453
.10.1243/JMES_JOUR_1969_011_056_02
32.
Runchal
,
A. K.
,
Spalding
,
D. B.
, and
Wolfshtein
,
M.
,
1969
, “
Numerical Solution of the Elliptic Equations for Transport of Vorticity, Heat, and Matter in Two-Dimensional Flow
,”
Phys. Fluids
,
12
, pp.
21
28
.10.1063/1.1692439
33.
Harlow
,
F. H.
, and
Welch
,
J. E.
,
1965
, “
Numerical Calculation of Time-Dependent Viscous Incompressible Flow With Free Surface
,”
Phys. Fluids
,
8
(
12
), pp.
2182
2189
.10.1063/1.1761178
34.
Barakat
,
H. Z.
, and
Clark
,
J. A.
,
1965
, “
Transient Natural Convection in Flows in Closed Containers
,”
University of Michigan, Mechanical Engineering Department, Heat Transfer Lab
, Technical Report No. 2.
35.
Wolfshtein
,
M.
,
1968
, “
Numerical Smearing in One Sided Difference Approximations to the Equations of Non Viscous Flow
,”
Department of Mechanical Engineering, Imperial College
,
London
, Report No. EF/TN/3.
36.
Hirt
,
C. W.
,
1968
, “
Heuristic Stability Theory for Finite-Difference Equations
,”
J. Comput. Phys.
,
2
(
4
), pp.
339
355
.10.1016/0021-9991(68)90041-7
37.
Spalding
,
D. B.
,
1972
, “
A Novel Finite-Difference Formulation for Differential Expressions Involving Both First and Second Derivatives
,”
Int. J Numer. Methods Eng.
,
4
, pp.
551
559
.10.1002/nme.1620040409
38.
Leonard
,
B. P.
,
1979
, “
A Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation
,”
Comput. Methods Appl. Mech. Eng.
,
19
(
1
), pp.
59
98
.10.1016/0045-7825(79)90034-3
39.
Raithby
,
G. D.
,
1976
, “
Skew-Upstream Differencing Schemes for Nearly-Steady Problems Involving Fluid Flow
,”
Comput. Methods Appl. Mech. Eng.
,
9
, pp.
153
164
.10.1016/0045-7825(76)90058-X
40.
van Leer
,
B.
,
1982
,
Flux-Vector Splitting for the Euler Equations (Lecture Notes in Physics, Vol. 170
),
Springer
,
Berlin
, pp.
507
512
.
41.
Harten
,
A.
,
1983
, “
High Resolution Schemes for Hyperbolic Conservation Laws
,”
J. Comput. Phys.
,
49
(
2
), pp.
357
393
.10.1016/0021-9991(83)90136-5
42.
Wolfshtein
,
M.
,
1968
, “
Turbulent Convection in Impinging Jets
,” Ph.D. thesis,
Imperial College, London University
,
London, UK
.
43.
Runchal
,
A. K.
,
1969
, “
Transport Processes in Steady Two-Dimensional Separated Flows
,” Ph.D. thesis,
Imperial College of Science and Technology
,
London, UK
.
44.
Gosman
,
A. D.
,
Pun
,
W. M.
,
Runchal
,
A. K.
,
Spalding
,
D. B.
, and
Wolfshtein
,
M.
,
1969
,
Heat and Mass Transfer in Recirculating Flows
,
Academic Press
,
London
.
45.
Edwards
,
A. L.
,
1968
, “
TRUMP: A Computer Program for Transient and Steady-State Temperature Distributions in Multi-Dimensional Systems
,”
Lawrence Radiation Laboratory, Univ. of California
,
Livermore, CA
, Report No. UCRL 14754.
46.
Roache
,
P. J.
,
1972
,
Computational Fluid Dynamics
,
Hermosa Publishers
, Socorro, NM.
47.
Spalding
,
D. B.
,
1980
, “
Idealisations of Radiation
,”
Imperial College, Mechanical Engineering Department
, Report No. HTS/2080/1.
48.
Caretto
,
L. S.
,
Curr
,
R. M.
, and
Spalding
,
D. B.
,
1972
, “
Two Numerical Methods for Three-Dimensional Boundary Layers
,”
Comput. Methods Appl. Mech. Eng.
,
1
(
1
), pp.
39
57
.10.1016/0045-7825(72)90020-5
49.
Chorin
,
A. J.
,
1967
, “
The Numerical Solution of the Navier-Stokes Equations for an Incompressible Fluid
,”
Bull. Am. Math. Soc.
,
73
(
6
), pp.
928
931
.10.1090/S0002-9904-1967-11853-6
50.
Patankar
,
S. V.
, and
Spalding
,
D. B.
,
1972
, “
A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows
,”
Int. J Heat Mass Transfer
,
15
, pp.
1787
1806
.10.1016/0017-9310(72)90054-3
51.
Van Doormaal
,
J. P.
, and
Raithby
,
J. P.
,
1984
, “
Enhancements of the Simple Method for Predicting Incompressible Fluid Flows
,”
Numer. Heat Transfer, Part B
,
7
(
2
), pp.
147
163
.10.1080/10407798408546946
52.
Patankar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
McGraw-Hill
,
New York
.
53.
Spalding
,
D. B.
,
1980
, “
Mathematical Modelling of Fluid Mechanics, Heat Transfer and Mass Transfer Processes
,”
Mechanical Engineering Department
, Imperial College, London, Technical Report No. HTS-80-1.
54.
Vanka
,
P.
,
1986
, “
Block-Implicit Multigrid Solution of Navier-Stokes Equations in Primitive Variables
,”
J. Comput. Phys.
,
65
(
1
), pp.
138
158
.10.1016/0021-9991(86)90008-2
55.
Runchal
,
A. K.
,
1971
, “
A Non-Staggered Finite-Difference Procedure for 3D Primitive Variable Navier-Stokes Equations and a Concise Notation for Difference Schemes
,” Mechanical Engineering Department, Imperial College, London, Technical Note: 3D-Duct Flow Group, July 15.
56.
Rhie
,
C. M.
, and
Chow
,
W. L.
,
1983
, “
Numerical Study of the Turbulent Flow Past an Airfoil With Trailing Edge Separation
,”
AIAA J.
,
21
(
11
), pp.
1525
1532
.10.2514/3.8284
57.
Kolmogorov
,
A. N.
,
1942
, “
Equations of Motion of an Incompressible Turbulent Fluid
,”
Izv Akad Nauk SSSR Ser Phys
,
6
, pp.
56
58
.
58.
Prandtl
,
L.
,
1945
, “
Ueber Ein Neues Formelsystem Fuer die Ausgebildete Turbulenz
,” Nachr. Akad. Wiss. Goettingen. II, Math.-Phys. Klasse,
6
, pp. 6–19.
59.
Chou
,
P. Y.
,
1945
, “
On the Velocity Correlations and the Solution of Equations of Turbulence Fluctuations
,”
Q. Appl. Math.
,
3
, pp.
38
54
.
60.
Rotta
,
J. C.
,
1951
, “
Statistische Theorie Nichthomogener Turbulenz
,”
Zeitschrift fur Physik, 129, pp. 547–572 and
131
, pp.
51
77
(Translated into English by W. Rodi as Imperial College Mechanical Engineering Department Technical Notes TWF/TN/38 and TWF/TN/39).
61.
Davidov
,
B. I.
,
1961
, “
On the Statistical Dynamics of an Incompressible Turbulent Fluid
,”
Dokl. AN SSR
,
136
(
1
), pp.
47
50
.
62.
Harlow
,
F. H.
, and
Nakayama
,
P. I.
,
1968
, “
Transport of Turbulence Energy Decay Rate
,”
Los Alamos Scientific Laboratory, University of California
, Report No. LA-3854.
63.
Hanjalic
,
K.
,
1970
, “
Two Dimensional Asymmetrical Turbulent Flow in Ducts
,” Ph.D. thesis,
Imperial College, London University
,
UK
.
64.
Jones
,
W. P.
, and
Launder
,
B. E.
,
1972
, “
The Prediction of Laminarization With a Two-Equation Model of Turbulence
,”
Int. J. Heat Mass Transfer
,
15
, pp.
301
314
.10.1016/0017-9310(72)90076-2
65.
Launder
,
B. E.
, and
Spalding
,
D. B.
,
1972
,
Mathematical Models of Turbulence
,
Academic Press
,
New York
.
66.
Launder
,
B. E.
, and
Spalding
,
D. B.
,
1974
, “
Computational Methods for Turbulent Flows
,”
Comput. Methods Appl. Mech. Eng.
,
3
, pp.
269
289
.10.1016/0045-7825(74)90029-2
67.
Saffman
,
P. G.
,
1976
, “
Development of a Complete Model for the Calculation of Turbulent Shear Flows
,”
Symposium on Turbulence and Dynamical Systems
,
Duke University
,
Durham, NC
.
68.
Wilcox
,
D. C.
,
2006
,
Turbulence Modeling for CFD
, 3rd ed.,
DCW Industries, Inc.
,
La Canada, California
.
69.
Spalding
,
D. B.
,
1971
, “
Mixing and Chemical Reaction in Confined Turbulent Flames
,”
13th International Symposium on Combustion
,
The Combustion Institute
, pp.
649
657
.
70.
Khalil
,
E. E.
,
Spalding
,
D. B.
, and
Whitelaw
,
J. H.
,
1975
, “
The Calculation of Local Flow Properties in Two-Dimensional Furnaces
,”
Int. J. Heat Mass Transfer
,
18
(
6
), pp.
775
791
.10.1016/0017-9310(75)90207-0
71.
Spalding
,
D. B.
,
1976
, “
Mathematical-Models of Turbulent Flames
,”
Combust. Sci. Technol
.,
13
(
1–6
), pp.
3
25
.10.1080/00102207608946727
72.
Lockwood
,
F. C.
, and
Naguib
,
A. S.
,
1975
, “
The Prediction of the Fluctuations in the Properties of Free, Round-Jet, Turbulent, Diffusion Flames
,”
Combust. Flame
,
24
, pp.
109
124
.10.1016/0010-2180(75)90133-9
73.
Elghobashi
,
S.
,
Spalding
,
D. B.
, and
Srivatsa
,
S. K.
,
1977
, “
Prediction of Hydrodynamics and Chemistry of Confined Turbulent Methane-Air Mixtures With Attention to the Formation of Oxides of Nitrogen
,” Report No. NASA CR-135170, CHAM TR 951/2.
74.
Spalding
,
D. B.
,
1978
, “
A General Theory of Turbulent Combustion
,”
J. Energy
,
2
(
1
), pp.
16
23
.10.2514/3.62362
75.
Serag-Eldin
,
M. A.
, and
Spalding
,
D. B.
,
1979
, “
Computations of Three-Dimensional Gas-Turbine Combustion Chamber Flows
,”
ASME J. Eng. Power
,
101
(
3
), pp.
326
336
.10.1115/1.3446580
76.
Spalding
,
D. B.
,
1979
, “
The Influences of Laminar Transport and Chemical Kinetics on the Time-Mean Reaction Rate in a Turbulent Flame
,”
Proceedings of the 17th Symposium (International) on Combustion
, pp.
431
440
.
77.
Spalding
,
D. B.
,
1976
, “
The ESCIMO Theory of Turbulent Combustion
,”
Department of Mechanical Engineering, Imperial College
,
London
, Report No. HTS/76/13.
78.
Kerstein
,
A. R.
,
1989
, “
Linear-Eddy Modeling of Turbulent Transport. II: Application to Shear Layer Mixing
,”
Combust. Flame
,
75
, pp.
397
413
.10.1016/0010-2180(89)90051-5
79.
Spalding
,
D. B.
,
1981
, “
IPSA New Developments and Computed Results
,”
Imperial College
, Report No. HTS/81/2.
80.
Spalding
,
D. B.
,
1980
, “
Numerical Computation of Multi-Phase Flow and Heat Transfer
,”
Recent Advances in Numerical Methods in Fluids
,
C.
Taylor
, ed.,
Pineridge Press
,
Swansea, UK
.
81.
Spalding
,
D. B.
,
1977
, “
The Calculation of Free-Convection Phenomena in Gas–Liquid Mixtures
,”
Heat Transfer and Turbulent Buoyant Convection, Vol. 2
,
D. B.
Spalding
and
N.
Afgan
, eds.,
Hemisphere
,
Washington, DC
.
82.
Spalding
,
D. B.
,
1974
, “
A Method for Computing Steady and Unsteady Flows Possessing Discontinuities of Density
,”
CHAM Ltd.
,
Wimbledon, London
, Report No. 910/2.
83.
Spalding
,
D. B.
, and
Malin
,
M. R.
,
1984
, “
A Two-Fluid Model of Turbulence and Its Application to Heated Plane Jets and Wakes
,”
PhysicoChem. Hydrodyn.
,
5
(
5–6
), pp.
339
361
.
84.
Ilegbusi
,
O. J.
, and
Spalding
,
D. B.
,
1989
, “
Prediction of Fluid Flow and Heat Transfer Characteristics of Turbulent Shear Flows With a Two-Fluid Model of Turbulence
,”
Int. J. Heat Mass Transfer
,
32
(
4
), pp.
767
774
.10.1016/0017-9310(89)90224-X
85.
Spalding
,
D. B.
,
1986
, “
The Two-Fluid Model of Turbulence Applied to Combustion Phenomena
,”
AIAA J.
,
24
(
6
), pp.
876
884
.10.2514/3.9362
86.
Spalding
,
D. B.
,
1987
, “
A Turbulence Model for Buoyant and Combusting Flows
,”
Int. J. Numer. Methods Eng.
,
24
(
1
), pp.
1
23
.10.1002/nme.1620240102
87.
Spalding
,
D. B.
,
1996
, “
Multi-Fluid Models of Turbulent Combustion
,”
CTAC95 Biennial Conference
,
Melbourne, Australia
,
World Scientific Publishing Co.
, pp.
59
81
.
You do not currently have access to this content.