References

1. Dolfin, http://www.fenics.org/dolfin.
2. F1 Nutter aerodynamics, http://www.f1nutter.co.uk/tech/aero.php.
3. F1

Country

aerodynamics,

http://www.f1-country.com/f1-engineer/

aeorodynamics/f1-aerodynamics.html.

4. Naca airfoil series, http://www.aerospaceweb.org/question/airfoils/q0041.

shtml.

5. PETSc, http://www-unix.mcs.anl.gov/petsc.
6. M. Ainsworth and J. T. Oden, A posteriori error estimation in finite ele-

ment analysis, Computat. Meth. Appl. Mech. Eng., 142 (1997), pp. 1–88.

7. L. W. Alaways, Aerodynamics of the curve-ball: and investigation of the

effects of angular velocity on baseball trajectories, PhD thesis, University of
California Davis, 1998.

8. I. Babuˇ

ska and A. D. Miller

, The post-processing approach in the finite

element method, i: Calculation of displacements, stresses and other higher
derivatives of the dispacements., Int. J. Numer. Meth. Eng., 20 (1984),
pp. 1085–1109.

9.

, The post-processing approach in the finite element method, ii: The calcu-

lation stress intensity factors., Int. J. Numer. Meth. Eng., 20 (1984), pp. 1111–
1129.

10.

, The post-processing approach in the finite element method, iii: A poste-

riori error estimation and adaptive mesh selection, Int. J. Numer. Meth. Eng.,
20 (1984), pp. 2311–2324.

11. B. Bagheri and L. R. Scott, Analysa, http://people.cs. uchicago.edu/

ridg/al/aa.html.

12. A. T. Bahill, D. G. Baldwin, and J. Venkateswaran, Predicting a base-

ball’s path, American Scientist, 93 (1980), pp. 218–225.

13. A. Bakker, R. D. LaRoche, M.-H. Wang, and R. V. Calabrese, Sliding

mesh simulation of laminar flow in stirred reactors, The Online CFM Book
(http://www.bakker.org/cfm), (1998).

14. R. Becker and R. Rannacher, A feed-back approach to error control in

adaptive finite element methods: Basic analysis and examples, East-West J.
Numer. Math., 4 (1996), pp. 237–264.

15.

, A posteriori error estimation in finite element methods, Acta Numer.,

10 (2001), pp. 1–103.

16. J. Bey, Tetrahedral grid refinement, Computing, 55 (1995), pp. 355–378.

390

References

17. P. Blossey, Book review of stability and transition in shear flows, SIAM

Review, 44(1) (2002).

18. L. Boltzmann, Lectures on Gas Theory, Dover, 1964.
19. M. Braack and T. Richter, Solutions of 3d Navier-Stokes benchmark

problems with adaptive finite elements, Computers and Fluids, 35(4) (2006),
pp. 372–392.

20. A. Brooks and T. Hughes, Streamline upwind/Petrov-Galerkin formulations

for convection dominated flows with particular emphasis on the incompressible
Navier-Stokes equations, Computer methods in applied mechanics and engi-
neering, 32 (1982), pp. 199–259.

21. S. Buijssen and S. Turek, University of Dortmund, private communication,

(2004).

22. S. Carnot, Reflections of the motive power of fire and on machines fitted to

develop that power, 1824.

23. M. J. Carr´

e, T. Asai, T. Akatsuka, and S. J. Haake

, The curve kick of

a football ii: flight through the air, Sports Engineering, 5 (2002), pp. 193–200.

24. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover, 1981.
25. B. A. Chipra, Tossed coins and troubled marriages: mathematical highlights

from aaas 2004, SIAM News (http://www.siam.org/pdf/news/217.pdf), 37(4)
(2004).

26. G. Constantinescu, M. Chapelet, and K. Squires, Turbulence modeling

applied to flow over a sphere, AIAA Journal, 41(9) (2003), pp. 1733–1742.

27. G. Constantinescu, R. Pacheco, and K. Squires, Detached-eddy simula-

tion of flow over a sphere, AIAA, 2002-0425 (2002).

28. G. Constantinescu and K. Squires, Numerical investigations of flow over

a sphere in the subcritical and supercritical regimes, Physics of Fluids, 16(5)
(2004), pp. 1449–1466.

29. J. d’Alembert, Essai d’une nouvelle th´

eorie de la r´

esistance des fluides, Paris,

http://gallica.bnf.fr/anthologie/notices/00927.htm, 1752.

30. J. Deng, T. Hou, and X. Yu, Geometric properties and nonblowup of 3d

incompressible Euler flow, Comm. in Partial Differential Equations, 30 (2005),
pp. 225–243.

31. P. Diaconis, S. Holmes, and R. Montgomery, Dynamical bias in the coin

toss, SIAM Review, (to appear).

32. J. Duchon and R. Robert, Inertial energy dissipation for weak solutions

of incompressible euler and Navier-Stokes solutions, Nonlinearity, (2000),
pp. 249–255.

33. T. Dupont, J. Hoffman, C. Johnson, R. Kirby, M. Larson, A. Logg,

and R. Scott

, The fenics project, Chalmers Finite Element Center Preprint

2003-21, Chalmers University of Technology, (2003).

34. H. Elman, D. Silvester, and A. Wathen, Finite elements and fast iterative

solvers: with applications in incompressible fluid dynamics, Oxford University
Press, Oxford, 2005.

35. K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, Introduction to adap-

tive methods for differential equations, Acta Numer., 4 (1995), pp. 105–158.

36. K. Eriksson, D. Estep, and C. Johnson, Applied Mathematics Body and

Soul: Vol I-III, Springer-Verlag Publishing, 2003.

37. K. Eriksson and C. Johnson, An adaptive finite element method for linear

elliptic problems, Math. Comp., 50 (1988), pp. 361–383.

References

391

38. L. Euler, Principes generaux du mouvements des fluides, l’Academie de

Berlin, 1755.

39. FEniCS, Fenics project, http://www.fenics.org, (2003).
40. L. Freitag and P. Knupp, Tetrahedral mesh improvement via optimization of

the element condition number, Intl. J. Numer. Meth. Engr., 53 (2002), pp. 1377–
1391.

41. U. Frisch, Turbulence - The Legacy of A. N. Kolmogorov, Cambridge Univer-

sity Press, 1995.

42. M. Germano, U. Poimelli, P. Moin, and W. Cabot, A dynamic subgrid

scale eddy-viscosity model, Phys. Fluids A, 3 (1991), p. 1760.

43. J. W. Gibbs, On the Equilibrium of Heterogeneous Substances (1875), The

Scientific Papers by J W Gibbs, Dover, 1961.

44. M. Giles, M. Larson, M. Levenstam, and E. S¨

uli

, Adaptive error control

for finite element approximations of the lift and drag coefficients in viscous
flow, Technical Report NA-76/06, Oxford University Computing Laboratory,
(1997).

45. M. Giles and E. S¨

uli

, Adjoint methods for pdes: a posteriori error analysis

and postprocessing by duality, Acta Numer., 11 (2002), pp. 145–236.

46. J. L. Guermond, Stabilization of Galerkin approximations of transport equa-

tions by subgrid modeling, M2AN, 33(6) (1999), pp. 1293–1316.

47. P. Hansbo, A Crank-Nicolson type space-time finite element method for com-

puting on moving meshes, Journal of Computational Physics, 159 (2000),
pp. 274–289.

48. P. Hansbo and A. Szepessy, A velocity-pressure streamline diffusion finite

element method for the incompressible Navier-Stokes equations, Computer
methods in applied mechanics and engineering, 84 (1990), pp. 175–192.

49. R. Hartmann and P. Houston, Goal-oriented a posteriori error estima-

tion for multiple target functionals, in Hyperbolic problems: theory, numerics,
applications, (T.Y. Hou and E. Tadmor, editors), pp. 579-588, Springer, 2003.

50. V. Heuveline and R. Rannacher, Duality-based adaptivity in the hp-finite

element method, J. Numer. Math., 11(2) (2003), pp. 95–113.

51. J. Heywood, Remarks on the possible global regularity of solutions of the three-

dimensional Navier-Stokes equations.

52. J. Hoffman, On duality based a posteriori error estimation in various norms

and linear functionals for les, SIAM J. Sci. Comput., 26(1) (2004), pp. 178–195.

53.

, Computation of mean drag for bluff body problems using adaptive

DNS/LES, SIAM J. Sci. Comput., 27(1) (2005), pp. 184–207.

54.

, Adaptive simulation of the turbulent flow past a sphere, J. Fluid Mech.,

(accepted).

55.

, Computation of turbulent flow past bluff bodies using adaptive general

galerkin methods: drag crisis and turbulent euler solutions, Comput. Mech., 38
(2006), pp. 390–402.

56.

, Efficient computation of mean drag for the subcritical flow past a circular

cylinder using General Galerkin G2, Int. J. Numer. Meth. Fluids, (accepted).

57.

, Adaptive simulation of the turbulent flow due to a cylinder rolling along

ground, (in review).

58. J. Hoffman and C. Johnson, Adaptive finite element methods for incom-

pressible fluid flow, Error Estimation and Solution Adaptive Discretization in
Computational Fluid Dynamics (Ed. T. J. Barth and H. Deconinck), Lecture

392

References

Notes in Computational Science and Engineering, Springer-Verlag Publishing,
Heidelberg, 2002, pp. 97–158.

59.

, A new approach to computational turbulence modeling, Comput. Meth-

ods Appl. Mech. Engrg., (in press).

60.

, Stability of the dual Navier-Stokes equations and efficient computation

of mean output in turbulent flow using adaptive DNS/LES, Comput. Methods
Appl. Mech. Engrg., (in press).

61.

, Finally: Resolution of d’alembert’s paradox, Finite Element Center

preprint (www.femcenter.org), (2006).

62.

, Is the world a clock with finite precision?, Finite Element Center

preprint (www.femcenter.org), (2006).

63. J. Hoffman, C. Johnson, and A. Logg, Dreams of Calculus: Perspectives

on Mathematics Education, Springer-Verlag Publishing, 2004.

64. J. Hoffman and A. Logg, Dolfin - dynamic object oriented library for fi-

nite element computation, Chalmers Finite Element Center Preprint 2002-06,
Chalmers University of Technology, (2002).

65. T. Hughes and T. Tezduyar, Finite element methods for first-order hyper-

bolic systems with particular emphasis on the compressible Euler equations,
Computer methods in applied mechanics and engineering, 45 (1984), pp. 217–
284.

66. T. J. R. Hughes, L. Mazzei, and K. E. Jansen, Large eddy simulation and

the variational multiscale method, Computer methods in applied mechanics and
engineering, 3 (2000), pp. 47–59.

67. V. John, Slip with friction and penetration with resistance boundary conditions

for the Navier–Stokes equations - numerical tests and aspects of the implemen-
tation, J. Comp. Appl. Math., 147 (2002), pp. 287–300.

68. V. John and A. Liakos, Time dependent flow across a step: the slip with

friction boundary condition, accepted for publication in Int. J. Numer. Meth.
Fluids, (2005).

69. C. Johnson, Adaptive Finite Element Methods for Conservation Laws, Ad-

vanced Numerical Approximation of Nonlinear Hyperbolic Equations, Springer
Lecture Notes in Mathematics, Springer Verlag, 1998, pp. 269–323.

70. C. Johnson, U. N¨

avert, and J. Pitk¨

aranta

, Finite element methods for

linear hyperbolic equations, Comput. Methods Appl. Mech. Eng., 45 (1984),
pp. 285–312.

71. C. Johnson and R. Rannacher, On error control in CFD, Int. Workshop

Numerical Methods for the Navier-Stokes Equations (F.K. Hebeker et.al. eds.),
Vol. 47 of Notes Numer. Fluid Mech., Vierweg, Braunschweig, 1994, pp. 133–
144.

72. C. Johnson, R. Rannacher, and M. Boman, Numerics and hydrodynamic

stability: Toward error control in CFD, SIAM J. Numer. Anal., 32 (1995),
pp. 1058–1079.

73. G.-S. Karamanos and G. E. Karniadakis, A spectral vanishing viscos-

ity method for large-eddy simulations, Journal of Computational Physics, 163
(2000), pp. 22–50.

74. A. N. Kolmogorov, Dissipation of energy in locally isotropic turbulence,

Dokl. Akad. Nauk SSSR, 32 (1941), pp. 16–18.

75.

, The local structure of turbulence in incompressible viscous fluid for very

large Reynolds number, Dokl. Akad. Nauk SSSR, 30 (1941), pp. 299–303.

References

393

76.

, On degeneration (decay) of isotropic turbulence in an incompressible

viscous liquid, Dokl. Akad. Nauk SSSR, 31 (1941), pp. 538–540.

77. S. Krajnovi´

c and L. Davidson

, Large-eddy simulation of the flow around a

bluff body, AIAA Journal, 40 (2002), pp. 927–936.

78. M. Landahl, A note on an algebraic instability of inviscid parallel shear flows,

J. Fluid Mech., 252 (1980), p. 209.

79. J. Leray, Sur le mouvement d’un liquide visqueux emplissant l’espace., Acta

Mathematica, 63 (1934), pp. 193–248.

80. M. Lesieur, Turbulence in Fluids, Kluwer Academic Publishers, London,

England, 1997.

81. J. Lions, Quelques m´

ethodes de r´

esolution des probl´

emes aux limites non lin-

eaires, Etudes mathematiques, Dunod Gauthiers-Villars, 1969.

82. A. Logg, Automation of Computational Mathematical Modeling, PhD thesis,

Chalmers, 2004.

83. E. Lorenz, Deterministic nonperiodic flow, J. Atmospheric Sciences, 20

(1963).

84. J. Loschmidt, Sitzungsber. kais. akad. wiss. wien, math., Naturwiss. Classe

73, (1876), pp. 128–142.

85. H. G. Magnus, On the derivation of projectiles; and on a remarkable pheno-

menon of rotating bodies, Memoirs of the Royal Academy, Berlin, Edited by
John Tyndall and William Francis, (1852), p. 210.

86. J. C. Maxwell, Phil. Trans. Royal Society, (1879).
87. P. Moin and J. Kim, Tackling turbulence with supercomputers, Scientific

American, (1997).

88. NASA, Various views of von karman vortices, http://disc.gsfc.nasa.gov/

oceancolor/scifocus/oceanColor/vonKarman vortices.shtml, (2005).

89. C. L. M. H. Navier, M´

emoire sur les lois du mouvement des fluiales, M´

em.

Acad. Royal Society, 6 (1823), pp. 389–440.

90. J. V. Neumann and R. D. Richtmyer, A method for the numerical calcula-

tion of hydrodynamic shocks, J. Appl. Phys., 21 (3) (1950).

91. H. Poincar´

e

, Science and Method, 1903, Dover 1982.aux limites non lin´

eaires,

Dunod, Paris, 1969.

92. Prandtl,

Prandtl

standard

view,

www.fluidmech.net/msc/prandtl.htm,

(2006).

93. L.

Prandtl

,

On

motion

of

fluids

with

very

little

viscosity,

Third

International Congress of Mathematics, Heidelberg, http://naca.larc.nasa.gov/
digidoc/report/tm/52/NACA-TM-452.PDF, (1904).

94. A. Quarteroni, What mathematics can do for the simulation of blood circu-

lation, EMS Proc. of the ICM 2006 Conference, Madrid. EMS 2006, (in press).

95. R. Rannacher, Finite element methods for the incompressible Navier–Stokes

equations, Preprint Intsitute of Applied Mathematics, Univ. of Heidelberg,
(1999).

96. B. Robins, New principles of gunnery containing the determination of the force

of gunpowder and investigation of the difference in the resisting power of the
air to swift and slow motion, 1742.

97. W. Rodi, J. H. Ferziger, M. Breuer, and M. Pourqui´

e

, Status of large

eddy simulation: Results of a workshop, ASME Journal of Fluids Engineering,
119 (1997), pp. 248–262.

394

References

98. P. Sagaut, Large Eddy Simulation for Incompressible Flows, Springer-Verlag,

Berlin, Heidelberg, New York, 2001.

99. H. Schlichting, Boundary Layer Theory, McGraw-Hill, 1955.

100. P. Schmid and D. Henningson, Stability and Transition in Shear Flows:

Applied Mathematical Sciences 142, Springer, 2001.

101. C. Schwab, p- and hp- Finite Element Methods Theory and Applications to

Solid and Fluid Mechanics, Oxford University Press, 1999.

102. T. K. Sengupta and S. B. Talla, Robins-maguns effect: a continuing saga,

Current Science, 86(7) (2004), pp. 1033–1036.

103. J. Smagorinsky, General circulation experiments with the primitive equations,

part i: The basic experiment, Mon. Wea. Rev., 91 (1963), p. 99.

104. A. Sommerfeld, Ein beitrag zur hydrodynamischen erkl¨

arung der turbulenten

߬

ussigkeitsbewegungen, Atti del 4. Congr. Internat.dei Mat. III, Roma, (1908),

pp. 116–124.

105. W. Thomson, On the dynamical theory of heat; with numerical results deduced

from mr. Joule’s equivalent of a thermal unit and M. Regnault’s observations
on steam, Math. and Phys. Papers, 1 (1851), p. 179.

106. D. J. Tritton, Physical Fluid Dynamics, 2nd ed. Oxford, Clarendon Press,

1988.

107. S. Turek, Efficient Solvers for Incompressible Flow Problems: An Algorithmic

and Computational Approach, Springer, Berlin, 1999.

108. R. Verf¨

urth

, A Review of A Posteriori Error Estimation and Adaptive Mesh

Refinement Teqniques, Wiley/Teubner, New York/Stuttgart, 1996.

109. Wikipedia,

Baseball

pitches,

http://en.wikipedia.org/wiki/Category:

Baseball pitches.

110. M. M. Zdravkovich, Flow around circular cylinders: a comprehensive guide

through flow phenomena, experiments, applications, mathematical models, and
simulations. Vol.1 [Fundamentals], Oxford Univ. Press, Oxford, 1997.

Index

-weak solution, 115
1st Law, 349, 360
2nd Law, 165, 349, 359, 369

a posteriori error estimate, 135, 249
ACMM, VII
adaptive algorithm, 225
Adaptive DNS/LES, 209, 225
adiabatic index, 40
ALE, 231
angle of attack, 182
approximate weak solution, 59

Bernoulli, 74
Bernoulli’s Law, 74, 76, 181, 297
bluff body flow, 245
Boltzmann, 384
boundary layer, 59, 279

Carnot, 349
Cayley, 34
CC, VII
cG(1)cG(1), 215
chaos, 97
chaotic dynamical system, 98
circular cylinder, 264
Clausius, 349
Clay Mathematics Institute, 113
compressible Euler, 357, 369
computability, 62
convective derivative, 42
Couette flow, 69, 313, 314

d’Alembert’s Mystery, 29, 33, 74

density, 39
deterministic chaos, 97
Dijkstra, 377
Direct Numerical Simulation, 57
dissipative weak solution, 164
DNS, 57
DOLFIN, 229
downforce, 195
drag coefficient, 58, 245
drag crisis, 176, 290
dual problem, 60, 119, 137, 247, 293
dynamical system, 47

eddy viscosity, 203
EG2, 111, 153, 292, 348, 351
Einstein, 383
entropy, 349
error representation, 121
Euler, 4, 177
Euler equations, 39, 43, 73, 151
existence, 113

FEniCS, 229
flat plate, 281
form drag, 245
free boundary, 233
friction boundary condition, 207, 216
Functional Analysis, 115

G2, 134, 153, 209
gas constant, 40
General Galerkin, 134

Hadamard, 115
harmonic oscillator, 101

396

Index

heat capacity, 40
heat conductivity, 46
horse shoe vortex, 250

ideal fluid, 39
ideal of Einstein, 47
incompressibility, 40, 42, 43, 211
internal energy, 40
inviscid fluid, 39
irreversibility, 347, 380
irrotational, 50

Joule’s experiment, 351

Kelvin-Planck, 349
Kolmogorov, 53
Kutta, 34
Kutta condition, 34
Kutta-Zhukovsky, 188

laminar boundary layer, 280
laminar flow, 51
Landahl, 306
Large Eddy Simulation, 201
Leonardo da Vinci, 33
Leray, 60, 113
LES, 201
lift coefficient, 58, 245
lift generation, 182
Lilienthal, 34
linearized Euler equations, 65
Lorenz, 97, 107
Loschmidt’s Mystery, 29, 111, 347

Mach number, 40
Magnus, 177
Magnus effect, 176, 297
mesh refinement, 227
mesh smoothing, 234
modal, 306
momentum, 39

Navier, 4
Navier–Stokes equations, 44, 114, 211
Neumann boundary condition, 213
Newton, 33
Newtonian, 4, 44, 211
no slip boundary condition, 213
non-modal, 70, 306
non-Newtonian fluids, 4

NS, 44, 114, 211

object in a box, 235
optimal perturbations, 330
outflow boundary condition, 213
output sensitivity, 119, 121

paradox, 29
phase averages, 257
phase jitter, 257
Planck, 385
Poiseuille flow, 313, 327
Poisson, 4
potential flow, 50, 76
Prandtl, 34, 81
predictability, 62
pressure, 39
pressure drag, 175, 245
Prize Problem, 113
probability, 103

randomness, 97
RANS, 201
rarefaction, 364
reattach, 285
recirculation, 285
regularity, 113
residual, 114, 154
reverse Magnus effect, 180
Reynolds, 51, 306
Reynolds number, 51
Reynolds stresses, 201
Robins, 177
Robins’ effect, 177

Saint-Venant, 4
Schlichting, 306
separation, 285
shock, 365
shock-capturing, 204, 213, 376
skin friction, 175, 245, 280
sliding mesh, 238
slip boundary condition, 213
Smagorinsky, 203
Smagorinsky model, 204
Sommerfeld, 306
Sommerfeld’s Mystery, 29, 70
speed of sound, 40
sphere, 275

Index

397

square cylinder, 257
stability factor, 60, 115
stabilized Galerkin method, 133
state equation, 40
statistical mechanics, 111, 385
Stokes, 4
strain rate tensor, 211
stress tensor, 211
surface mounted cube, 250

Taylor-G¨

ortler mechanism, 327

temperature, 40, 162
test function, 114, 211, 215
thermodynamics, 348
total energy, 39
transition, 51, 305
turbulent boundary layer, 176, 281

turbulent flow, 51

uniqueness, 113

velocity, 39
velocity potential, 50
viscosity, 44
von K´

arm´

an, 264

von K´

arm´

an vortex street, 264

vorticity, 78

wall modeling, 207
weak uniqueness, 60, 121, 125
well-posed, 116
Wright, 35

Zhukovsky, 35