References

1

P. Roach. Computational Fluid Dynamics. Hermosa Publishing, 1972.

2

J. Connor and C. Brebbia. Finite Element Techniques for Fluid Flow. Newnes-Butterworths, 1976.

3

J. Dupuy and A. Dianoux. Microscopic Structure and Dynamics of Liquids. Plenum Press, 1978.

4

J. Goodfellow. Molecular Dynamics. Macmillan Press, 1991.

5

U. Frisch, B. Hasslacher, and Y. Pomeau. Lattice-gas automata for the Navier-Stokes equation. Physical Review Letters, 56:1505-1508, 1986.

6

P. L. Bhatnagar, E. P. Gross, and M Krook. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Physical Review, 94 (3):511-525, 1954.

7

J. Buick, W. Easson, and C. Greated. Simulation of wave motion using a lattice gas model. International Journal for Numberical Methods in Fluids, 22:313-321, 1996.

8

U. Frisch, D. d' Humières, B. Hasslacher, P. Lallemand, and Y. Pomeau. Lattice gas hydrodynamics in two and three dimensions. Complex Systems, 1:649-707, 1987.

9

E. Orlandini, M. R. Swift, and J. M. Yeomans. A lattice Boltzmann model of binary-fluid mixtures. Europhysics Letters, 32 (6):463-468, 1995.

10

A. J.. Martin, W. J. Easson, and C. A. Greated. Experimental study of oceanic internal waves using particle image velocimetry. In ISOPE 95, Delft, 1995.

11

S. Chapman and T. G. Cowling. The Mathematical Theory of Non-Uniform Gases. Cambridge University Press, 1970.

12

C. Cercignani. Theory and Application of the Boltzmann Equation. Scottish Academic Press, 1975.

13

S. Harris. An Introduction to the Theory of The Boltzmann Equation. Holt, Rinehart and Winston INC., 1970.

14

L. E. Reichl. A Modern Course in Statistical Physics. Edward Arnold (Publishing) LTD, 1980.

15

E. G. D. Cohen. Fifty years of kinetic theory. Physica A, 194:229-257, 1993.

16

J. Hardy, Y. Pomeau, and O. de Pazzis. Time evolution of two-dimensional model system I: invariant states and time correlation functions. Journal of Mathematical Physics, 14:1746-1759, 1973.

17

J. Hardy, O. de Pazzis, and Y. Pomeau. Molecular dynamics of a classical lattice gas: Transport properties and time correlation functions. Physics Review A, 13:1949-1961, 1976.

18

A. K. Gunstensen and D. H. Rothman. A Galilean-invariant immiscible lattice gas. Physica D, 47:53-63, 1991.

19

D. d' Humières, P. Lallemand, and G. Searby. Numerical experiments on lattice gases: Mixtures and Galilean invariance. Complex Systems, 1:633-647, 1987.

20

D. d' Humières, P. Lallemand, and U Frisch. Lattice gas models for 3D hydrodynamics. Europhysics Letters, 2:291-297, 1986.

21

R. Cornubert, D. d' Humières, and D. Levermore. A Knudsen later theory for lattice gases. Physica D, 47:241-259, 1991.

22

M. Hénon. In [8].

23

M. Hénon. Viscosity of a lattice gas. Complex Systems, 1:763-789, 1987.

24

S. Wolfram. Cellular automaton fluids 1: Basic theory. Journal of Statistical Physics, 45(3/4):471-529, 1986.

25

P. Clavin, P. Lallemand, Y. Pomeau, and G. Searby. Simulations of free boundaries in flow systems by lattice-gas models. Journal of Fluid Mechanics, 188:437-464, 1988.

26

A. K. Gunstensen and D. H. Rothman. A lattice-gas model for three immiscible fluids. Physica D, 47:47-52, 1991.

27

V. Zehnlé and G Searby. Lattice gas experiments on a non-exothermic flame in a vortex field. Le Journal De Physique France, 50:1083-1097, 1989.

28

D. H. Rothman and J. M. Keller. Immiscible cellular-automaton fluids. Journal of Statistical Physics, 52:1119-1127, 1988.

29

C. Appert and S Zaleski. Lattice gas with a liquid-gas transition. Physical Review Letters, 64:1-4, 1990.

30

C. Appert, D Rothman, and S Zaleski. A liquid-gas model on a lattice. Physica D, 47:85-96, 1991.

31

D. d' Humières and P. Lallemand. Flow of a lattice gas between two parallel plates and development of the Poiseuille profile. Computes Rendus de L'Académie des Sciences Paris, 302:983, 1986.

32

D. d' Humières, Y. Pomeau, and P. Lallemand. Simulation of 2-D Von Karman streets using a lattice gas. Computes Rendus de L'Académie des Sciences Paris, 301:423-426, 1985.

33

D. d' Humières and P. Lallemand. Lattice gas automata for fluid mechanics. Physica A, 140:326-335, 1986.

34

J. P. Boon and A. Noullez. Lattice gas hydrodynamics. In Special Course on Modern Theoretical and Experimental Approaches to Turbulent Flow Structure and its Modelling. AGARD (Advisory Group for Aerospace Research and Development) NATO, 1987.

35

B. Wylie. Application of Two-Dimensional Cellular Automaton Lattice-Gas Models to the Simulation of Hydrodynamics. PhD thesis, The University of Edinburgh, 1990.

36

R. Kenway, D. McComb, and B. Wylie. Results reproduced in [95].

37

G. Searby, V Zenlé, and B Denet. Lattice gas mixtures and reactive flows. In Discrete Kinetic Theory, Lattice Gas Dynamics and the Foundations of Hydrodynamics, Torino, Italy, September 1988.

38

M. R. Swift, E. Orlandini, W. R. Osborn, and J. M. Yeomans. Lattice Boltzmann simulation of liquid-gas and binary fluid systems. Physical Review E, 54 (5):5041-5052, 1996.

39

G. R. McNamara and G. Zanetti. Use of the Boltzmann equation to simulate lattice-gas automata. Physical Review Letters, 61:2332-2335, 1988.

40

F. J. Higuera and J. Liménez. Boltzmann approach to lattice gas simulations. Europhysics Letters, 9 (7):663-668, 1989.

41

F. J. Higuera, S. Succi, and R. Benzi. Lattice gas dynamics with enhanced collisions. Europhysics Letters, 9 (4):345-349, 1989.

42

M. Vergassola R. Benzi and S. Succi. On the hydrodynamic behaviour of the lattice Boltzmann equation. Europhysics Letters, 13 (5):411-416, 1990.

43

S. Chen, H. Chen, D. Martinez, and W. Matthaues. Lattice Boltzmann model for simulation of magnetohydrodynamics. Physical Review Letters, 67 (27):3776-3779, 1991.

44

Y. H. Qian, D. d' Humières, and P Lallemand. Lattice BGK models for Navier-Stokes equation. Europhysics Letters, 17 (6):479-484, 1992.

45

H. Chen, S. Chen, and H. Matthaeus. Recovery of the Navier-Stokes equation using a lattice-gas Boltzmann method. Physical Review A, 45 (8):5339-5342, 1992.

46

S. Chen, Z. Wang, X. Shan, and G. D. Doolen. Lattice Boltzmann computational fluid dynamics in three dimensions. Journal of Statistical Physics, 68 (3/4):379-400, 1992.

47

R. D. Kingdon. A lattice BGK model for mimicking the Navier-Stokes equation for fluid flow in two dimensions. Technical Report AEA-InTec-1298, AEA Technology, 1993.

48

l. D. Landau and E. M. Lifschitz. Fluid Mechanics. Pergamon, 1987.

49

D. P. Ziegler. Boundary conditions for lattice Boltzmann simulations. Journal of Statistical Physics, 71 (5/6):1171-1177, 1993.

50

D. R. Noble, J. G. Georgiadis, and R. O. Buckius. Direct assessment of lattice Boltzmann hydrodynamics and boundary conditions for recirculating flows. Journal of Statistical Physics, 81 (1/2):17-33, 1995.

51

D. R. Noble, S. Chen, J. G. Georgiadis, and R. O. Buckius. A consistent hydrodynamic boundary condition for the lattice Boltzmann method. Physics of Fluids, 7 (1):203-209, 1995.

52

P. A. Skordos. Initial and boundary conditions for the lattice Boltzmann method. Physical Review E, 48 (6):4823-4842, 1993.

53

O. Behrand. Solid-fluid boundaries in particle suspension simulations via the lattice Boltzmann method. Physical Review E, 52 (1b):1164-1175, 1995.

54

A. J. C. Ladd. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. Journal of Fluid Mechanics, 271:285-309, 1994.

55

A. J. C. Ladd. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. Journal of Fluid Mechanics, 271:311-339, 1994.

56

A. K. Gunstensen, D. H. Rothman, A. Zaleski, and G. Zanetti. Lattice Boltzmann model of immiscible fluid. Physical Review A, 43 (8):4320-4327, 1991.

57

D. Grunau, S. Chen, and K. Eggert. A lattice Boltzmann model for multi-phase fluid flow. Physics of Fluids A, 5 (10):2557-2562, 1993.

58

I. Halliday and C. M. Care. Steady state hydrodynamics of a lattice Boltzmann immiscible lattice gas. Physical Review E, 53 (2):1602-1612, 1996.

59

E. G. Flekkøy. Lattice Bhatnagar-Gross-Krook models for miscible fluids. Physical Review E, 47 (6):4247-4257, 1993.

60

X. Shan and H. Chen. Lattice Boltzmann model for simulating flows with multiple phases and components. Physical Review E, 47:1815-1819, 1993.

61

X. Shan and H. Chen. Simulation of non-ideal gases and liquid-gas phase transitions by a lattice Boltzmann equation. Physical Review E, 49 (4A):2941-2948, 1994.

62

X. Shan and G. Doolen. Multi-component lattice-Boltzmann model with interparticle interactions. Journal of Statistical Physics, 81 (1-2):379-393, 1995.

63

M. R. Swift, W. R. Osborn, and J. M. Yeomans. Lattice Boltzmann simulation of nonideal fluids. Physical Review Letters, 75 (5):830-833, 1995.

64

J. P. Gunton, M. San Miguel, and P. S. Sahni. The dynamics of first-order phase transitions. In Phase Transitions and Critical Phenomena, editors, C. Domb and J. L. Lebowitz, volume 8. Academic Press New York, 1983.

65

J. S. Rowlinson and B. Widom. Molecular Theory of Capillarity. Clarendon Press, Oxford, 1982.

66

N. S. Martys and H. Chen. Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method. Physical Review E, 53 (1):743-750, 1996.

67

J. Lighthill. Waves In Fluids. Cambridge University Press, 1978.

68

J. S. Turner. Buoyancy Effects in Fluids. Cambridge University Press, 1973.

69

O. M. Phillips. The Dynamics of the Upper Ocean. Cambridge University Press, 1969.

70

J. Turner. Buoyancy Effects In Fluids. Cambridge University Press, 1973.

71

Ø. Arnsten. Uniform Stratified Flow Interaction with a Submerged Horizontal Cylinder - a Revisit of `deadwater' in a Norwegian Fjord. PhD thesis, University of Trondheim (Norwegian Institute of Technology), 1990.

72

R. Courant and D. Hilbert. Methods in Mathematical Physics. Interscience, 1953.

73

Routine D02KEF. The NAG Fortran Library, Mark 14, 1990.

74

W. J. Harrison. The influence of viscosity on the oscillations of superposed fluids. Proceedings of the London Mathematical Society, (2) 6:396-405, 1908.

75

H. Lamb. Hydrodynamics. Cambridge University Press, 1962.

76

J. N. Hunt. The viscous damping of gravity waves in shallow water. La Houille Blanche, 6:345-349, 1964.

77

B. Johns. A boundary layer method for the determination of the viscous damping of small amplitude gravity waves. Quarterly Journal of Mechanics and Applied Mathematics, 21 (1):93-103, 1968.

78

R. G. Dean and R. A. Dalrymple. Water Wave Mechanics for Engineers and Scientists. Prentice-Hall Inc., New Jersey, 1984.

79

C. C. Mei and L.-F. Liu. The damping of surface gravity waves in a bounded liquid. Journal of Fluid Mechanics, 59 (2):239-256, 1973.

80

R. A. Dalrymple and P. L.-F. Liu. Waves over soft muds: A two-layer fluid model. Journal of Physical Oceanography, 8:1121-1131, 1978.

81

P. L-F. Liu. Damping of water waves over porous bed. Journal of the Hydraulics Division, 99:2263-2271, 1973.

82

Routine E04HFF. The NAG Fortran Library, Mark 14, 1990.

83

P. E. Gill and W. Murry. Algorithms for the solution of the nonlinear least-squares problem. SIAM Journal of Numerical Analysis, 15:977-992, 1978.

84

Routine C04ADF. The NAG Fortran Library, Mark 14, 1990.

85

S. A. Thorpe. On standing internal gravity waves of finite amplitude. Journal of Fluid Mechanics, 32(3):489-528, 1968.

86

S. A. Thorpe. On the shape of progressive internal waves. Philosophical Transactions A, 263:563-614, 1968.

87

Y. Yeh and H. Z. Cummins. Localized fluid flow measurements with an He-Ne laser spectrometer. Applied Physics Letters, 4(10):176-178, 1964.

88

T. S. Durrani and C. A. Greated. Laser Systems in Flow Measurement. Plenum Press, 1977.

89

T. J. McDougall. On the elimination of refractive index variations in turbulent density stratified flows. Journal of Fluid Mechanics, 93:83-93, 1979.

90

I. A. Hannoun, H. J. S. Fernando, and E. J. List. Turbulent structure near a sharp density interface. Journal of Fluid Mechanics, 189:189-209, 1988.

91

I. A. Hannoun and E. J. List. Turbulent mixing at a shear free density interface. Journal of Fluid Mechanics, 189:211-234, 1988.

92

C. Gray and C. A. Greated. The application of particle image velocimetry to the study of water waves. Optics and Lasers in Engineering, 9:265-276, 1988.

93

C. Gray, C. A. Greated, D. R. McClusky, and W. J. Easson. An analysis of the scanning beam PIV illumination system. Journal of Physics E, 2:717-724, 1991.

94

C. Gray and C. A. Greated. Evolution of the particle image velocimetry flow measuring technique. Strain, pages 3-8, 1995.

95

D. Wallace. Scientific computation on simd and mimd machines. Philosophical Transactions of the Royal Society of London A, 326:481-498, 1988.

96

D. d' Humières and P. Lallemand. Numerical simulations of hydrodynamics with lattice gas automata in two dimensions. Complex Systems, 1:599, 1987.