Chapter 1 The Boltzmann equation and fluid dynamics

Handbook of Mathematical Fluid Dynamics

Volumn 1, Issue , 2002, Pages 1-69

  Cercignani, C ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67649306446     PISSN: 18745792     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-5792(02)80003-9     Document Type: Chapter

References (179)

1. Allegre J., and Bisch D. Experimental study of a blunted cone at rarefied hypersonic conditions. CNRS Report RC (1994) 94-7
2. Alsmeyer H. Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam. J. Fluid Mech. 74 (1976) 497-513
3. submitted to. Andries P., Le Tallec P., Perlat J.P., and Perthame B. The Gaussian-BGK model of Boltzmann equation with small Prandtl number. Eur. J. Mech. B. (2000)
4. Aristov V., and Tcheremissine F.G. The conservative splitting method for solving the Boltzmann equation. U.S.S.R. Comput. Math. Math. Phys. 20 (1980) 208-225
5. Arkeryd L. On the Boltzmann equation. Part II: The full initial value problem. Arch. Rational Mech. Anal. 45 (1972) 17-34
6. Arkeryd L., and Cercignani C. On a functional equation arising in the kinetic theory of gases. Rend. Mat.Ace. Lincei 9 11 (1990) 139-149
7. Babovsky H. A convergence proof for Nanbu 's Boltzmann simulation scheme. Eur. J. Mech. B. 8 1 (1989) 41-55
8. Babovsky H., and Illner R. A convergence proof for Nanbu's simulation method for the full Boltzmann equation. SIAM J. Numer. Anal. 26 (1989) 45-65
9. Bardos C., and Ukai S. The classical incompressible Navier-Stokes limit of the Boltzmann equation. Math. Models Methods Appl. Sci. 1 (1991) 235-257
10. Barwinkel K., and Schippers S. Nonreciprocity in noble-gas metal-surface scattering. In: Muntz E.P., Weaver D.P., and Campbell D.H. (Eds). Rarefied Gas Dynamics: Space-Related Studies (1989), AIAA 487-501
11. in Russian. Belotserkovskii O.M., and Yanitskii V. Statistical particle-in-cell method for solving rarefied gas dynamics problems. Zh. Vychisl. Mat. i Mat. Fiz. 15 (1975) 1195-1203
12. Benettin G., Galgani L., and Giorgilli A. Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part I. Comm. Math. Phys. 113 (1987) 87-103
13. Benettin G., Galgani L., and Giorgilli A. Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part II. Comm. Math. Phys. 121 (1989) 557-601
14. Bhatnagar P.L., Gross E.R., and Krook M. A model for collision processes in gases. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94 (1954) 511-525
15. Bird G.A. Shock wave structure in a rigid sphere gas. In: deLeeuw J.H. (Ed). Rarefied Gas Dynamics (1965), Academic Press, Washington 216-222
16. Bird G.A. Aspects of the structure of strong shock waves. Phys. Fluids 13 (1970) 1172-1177
17. Bird G.A. Direct Simulation of the Boltzmann equation. Phys. Fluids 13 (1970) 2676-2681
18. Bird G.A. Simulation of multi-dimensional and chemically reacting flows. In: Campargue R. (Ed). Rarefied Gas Dynamics (1979), CEA, New York 365-388
19. Bird G.A. Monte-Carlo simulation in an engineering context. Rarefied Gas Dynamics, Part I (1981), AIAA, Paris 239-255
20. Bird G.A. Molecular Gas Dynamics and the Direct Simulation of Gas Flows (1994), Clarendon Press, Washington
21. Bird G.A. The initiation of centrifugal instabilities in an axially symmetric flow. In: Shen C. (Ed). Rarefied Gas Dynamics Symposium 20 (1997), Peking Univ. Press, Oxford 624-629
22. Blanchard R.C. Rarefied flow lift to drag measurement of the Shuttle Orbiter. Paper No. ICAS 86-118.10.1. 15th ICAS Congress, London (September) (1986)
23. Boltzmann L. Weitere Studien tiber das Wdrmegleichgewicht unter Gasmolekulen. Sitzungsber. Akad. Wiss. II 66 (1872) 275-370
24. Boltzmann L. Neuer Beweis zweier Sätze über das Wärmegleichgewicht unter mehratomigen Gas-molekulen. Sitzungsber. Akad. Wiss. 95 (1887) 153-164
25. Boltzmann L. On certain questions of the theory of gases. Nature 51 (1895) 413-415
26. Leipzig. Boltzmann L. Vorlesungen über Gastheorie. J.A. Barth (1895-1898)
27. Borgnakke C., and Larsen P.S. Statistical collision model for Monte Carlo simulation of polyatomic gas mixture. J. Comput. Phys. 18 (1975) 405-420
28. Bryan G.H. Rep. Br. Ass. Advant. Sci. 83 (1894)
29. Celenligil M.C., and Moss J.N. Hypersonic rarefied flow about a delta wing - direct simulation and comparison with experiment. AIAA J. 30 (1992) 2017-2023
30. Cercignani C. Plane Poiseuille flow and Knudsen minimum effect. In: Laurman J.A. (Ed). Rarefied Gas Dynamics (1963), Academic Press, Beijing 92-101
31. Cercignani C. Reply to the comments by A.S. Berman. Phys. Fluids 10 (1967) 1859-1860
32. Cercignani C. Stokes paradox in kinetic theory. Phys. Fluids 11 (1968) 303-308
33. Cercignani C. A variational principle for boundary value problems in kinetic theory. J. Statist. Phys. 1 (1969) 297-311
34. Cercignani C. Boundary value problems in linearized kinetic theory. In: Bellman R., Birkhoff G., and Abu-Shumays I. (Eds). Transport Theory (1969), Amer. Math. Soc, New York 249-268
35. revised edition 1990. Cercignani C. Mathematical Methods in Kinetic Theory (1969), Plenum Press, Providence, RI
36. Cercignani C. On the Boltzmann equation for rigid spheres. Transport Theory Statist. Phys. (1972) 211-225
37. Cercignani C. Scattering kernels for gas-surface interactions. Transport Theory Statist. Phys. 2 (1972) 27-53
38. Cercignani C. Models for gas-surface interactions: comparison between theory and experiment. In: Dini D., et al. (Ed). Rarefied Gas Dynamics (1974), Editrice Tecnico-Scientifica, New York 75-96
39. Cercignani C. The Boltzmann Equation and its Applications (1988), Springer, Pisa
40. Cercignani C. Are there more than five linearly independent collision invariants for the Boltzmann equation?. J. Statist. Phys. 58 (1990) 817-824
41. Cercignani C. Scattering kernels for gas-surface interaction. Proceedings of the Workshop on Hypersonic Flows for Reentry Problems (1990), INRIA, New York 9-29
42. Cercignani C. Ludwig Boltzmann. The Man Who Trusted Atoms (1998), Oxford Univ. Press, Antibes
43. Cercignani C. Rarefied Gas Dynamics: From Basic Principles to Actual Calculations (2000), Cambridge Univ. Press, Oxford
44. Cercignani C., and Daneri A. Flow of a rarefied gas between two parallel plates. J. Appl. Phys. 34 (1963) 3509-3513
45. Cercignani C., and Frezzotti A. Numerical simulation of supersonic rarefied gas flows past a flat plate: effects of the gas-surface interaction model on the flow-field. In: Muntz E.P., Weaver D.P., and Campbell D.H. (Eds). Rarefied Gas Dynamics: Theoretical and Computational Techniques (1989), AIAA, Cambridge 552-566
46. Cercignani C., Frezzotti A., and Grosfils P. The structure of an infinitely strong shock wave. Phys. Fluids 11 (1999) 2757-2764
47. Cercignani C., Illner R., and Pulvirenti M. The Mathematical Theory of Dilute Gases (1994), Springer, Washington
48. Cercignani C., and Lampis M. Kinetic models for gas-surface interactions. Transport Theory Statist. Phys. 1 (1971) 101-114
49. Cercignani C., and Lampis M. Free molecular flow past a flat plate in the presence of a nontrivial gas-surface interaction. J. Appl. Math. Phys. (ZAMP) 23 (1972) 715-728
50. Cercignani C., and Lampis M. Influence of gas-surface interaction on drag and lift in free-molecular flow. Entropie 44 (1972) 40-46
51. Cercignani C., and Lampis M. On the H-theorem for polyatomic gases. J. Statist. Phys. 26 (1981) 795-801
52. Cercignani C., and Lampis M. A new model for the differential cross-section of a polyatomic gas. In: Shen C. (Ed). Rarefied Gas Dynamics (1997), Peking Univ. Press, New York 731-736
53. Cercignani C., and Lampis M. New scattering kernel for gas-surface interaction. AIAA J. 35 (1997) 1000-1001
54. Cercignani C., Lampis M., and Lentati A. A new scattering kernel in kinetic theory of gases. Transport Theory Statist. Phys. (1995) 1319-1336
55. Cercignani C., Lampis M., and Struckmeier J. Applications of a new model for the differential cross section of a classical polyatomic gas. Transport Theory Statist. Phys. 29 (2000) 355-374
56. Cercignani C., Lampis M., and Struckmeier J. New models for the differential cross section of a polyatomic gas in the frame of the scattering kernel theory. Mech. Res. Comm. 25 (1998) 231-236
57. Cépaduès éditions. Cercignani C., Lampis M.C., and Struckmeier J. Homogeneous relaxation and shock wave structure for a polyatomic gas. Toulouse. In: Brun R., Campargue R., Gatignol R., and Lengrand J.-C. (Eds). Rarefied Gas Dynamics (1999) 61-68
58. Cercignani C., and Pagani C.D. Variational approach to boundary-value problems in kinetic theory. Phys. Fluids 9 (1966) 1167-1173
59. Cercignani C., Pagani C.D., and Bassanini P. Flow of a rarefied gas past an axisymmetric body. II. Case of a sphere. Phys. Fluids 11 (1968) 1399-1403
60. Cercignani C., and Stefanov S. Bénard's instability in Kinetic Theory. Transport Theory Statist. Phys. 21 (1992) 371-381
61. Cercignani C., and Tironi G. Alcune applicazioni di un nuovo modello linearizzato dell'equazione di Boltzmann. Atti del Congresso Nazionale AIDA-AIR 1965 (1967), AIDA-AIR, Beijing 174-181
62. Cercignani C., and Tironi G. Nonlinear heat transfer between two parallel plates at large temperature ratios. In: Brundin C.L. (Ed). Rarefied Gas Dynamics (1967), Academic Press 441-453
63. Chanetz B. Study of axisymmetric shock wave-boundary layer interaction in hypersonic laminar flow. ONERA Report RT 42/4365 AN (1995)
64. Chapman S., and Cowling T.G. The Mathematical Theory of Non-Uniform Gases (1940), Cambridge Univ. Press, New York
65. Cheng H.K., Chen S.Y., Mobly R., and Huber C. On the hypersonic leading-edge problem in the merged-layer regime. In: Trilling L., and Wachman H.Y. (Eds). Rarefied Gas Dynamics (1969), Academic Press, London 1451-1463
66. Chow W.L. Hypersonic rarefied flow past the sharp leading-edge of a flat plate. AIAA J. 5 (1967) 1549-1557
67. Chow W.L. Hypersonic slip flow past the sharp leading-edge of a flat plate. AIAA J. 4 (1968) 2062-2063
68. Cowling T.G. On the Cercignani-Lampis formula for gas-surface interactions. J. Phys. D. Appl. Phys. 7 (1974) 781-785
69. Dahler J.S., and Sather N.F. Kinetic theory of loaded spheres. I. J. Chem. Phys. 38 (1962) 2363-2382
70. J.-S. Darrozès and J.-P. Guiraud, Généralisation formelle du théorème H en présence de parois. Applications, C. R. Acad. Sci. Paris Ser. A 262, 1368-1371.
71. De Masi A., Esposito R., and Lebowitz J.L. Incompressible Navier-Stokes equations and Euler limit of the Boltzmann equation. Comm. Pure Appl. Math. 42 (1989) 1189-1214
72. Rep. 78. Deshpande S.M. Dept. Aero. Engng. (1978), Indian Inst. Science, NewYork
73. Emanuel G. Bulk viscosity of a dilute polyatomic gas. Phys. Fluids A 2 (1990) 2252-2254
74. Enskog D. Kinetische theorie der Vorgänge in mässig verdünnten Gasen. I. Allgemeiner Teil (1917), Almqvist and Wiksell
75. Ferziger J.H., and Kaper H.G. Mathematical Theory of Transport Processes in Gases (1972), North-Holland, Uppsala
76. Garcia A.L. Nonequilibrium fluctuations studied by a rarefaction simulation. Phys. Rev. A 34 (1986) 1454-1457
77. Garcia A. Hydrodynamic fluctuations and the direct-simulation Monte Carlo method. In: Mareschal M. (Ed). Microscopic Simulations of Complex Flows (1990), Plenum Press, Amsterdam 177-188
78. Garcia A., and Penland C. Fluctuating hydrodynamics and principal oscillation pattern analysis. J. Statist. Phys. 164 (1991) 1121-1132
79. Providence, RI. Grad H. Singular and non-uniform limits of solutions of the Boltzmann equation. In: Bellman R., Birkhoff G., and Abu-Shumays I. (Eds). Transport Theory. Amer. Math. Soc. (1969) 269-308
80. Gropengieβer F., Neunzert N., and Struckmeier J. Computational methods for the Boltzmann equation. In: Spigler R. (Ed). Venice 1989: The State of Art in Applied and Industrial Mathematics (1990), Kluwer, New York 111-140
81. Hanson F.B., and Morse T.F. Kinetic models for a gas with internal structure. Phys. Fluids 10 (1967) 345-353
82. Harbour P.J., and Lewis J.H. Preliminary measurements of the hypersonic rarefied flow field on a sharp plate using an electron beam probe. In: Brundin C.L. (Ed). Rarefied Gas Dynamics (1967), Academic Press, Dordrecht 1031-1046
83. Harvey J.K. Direct simulation Monte Carlo method and comparison with experiment. Progr. in Astro, and Aero. 103 (1986) 25-42
84. Hassan H.A., and Hash D.B. A generalized hard-sphere model for Monte Carlo simulations. Phys. Fluids A 5 (1993) 738-744
85. Hilbert D. Begründung der kinetichen Gastheorie. Math. Ann. 72 (1912) 562-577
86. Hirschfelder J.O., Curtiss C.F., and Bird R.B. Molecular Theory of Gases and Liquids (1954), Wiley, New York
87. Harvard. Holway Jr. L.H. Approximation procedures for kinetic theory. PhD thesis (1963)
88. Huang A.B. Kinetic theory of the rarefied supersonic flow over a finite plate. In: Trilling L., and Wachman H.Y. (Eds). Rarefied Gas Dynamics (1969), Academic Press, New York 529-544
89. Huang A.B., and Hwang P.F. Kinetic theory of the sharp leading-edge flow, II. IAF Paper RE 63 October (1968)
90. Huang A.B., and Hwang P.F. Supersonic leading-edge problem according to the ellipsoidal model. Phys. Fluids 13 (1970) 309-317
91. Hurlbut F., and Sherman F.S. Application of the Nocilla wall reflection model to free-molecule kinetic theory. Phys. Fluids 11 (1968) 486-496
92. Ivanov M.S., Gimelshein S.F., and Beylich A.E. Hysteresis effect in stationary reflection of shock waves. Phys. Fluids A 7 (1995) 685-687
93. Ivanov M.S., Gimelshein S.F., and Markelov G.N. Statistical simulation of the transition between regular and Mach reflection in steady flows. Comput. Math. Appl. 35 (1998) 113-125
94. Jeans J.H. On the partition of energy in a system of loaded spheres. Q. J. Pure Appl. Math. 35 (1904) 224-238
95. Joss W.W., Vas I.E., and Bogdonoff S.M. Hypersonic rarefied flow over a flat plate. AIAA Paper 68-5 January (1968)
96. Kersch A., and Morokoff W.J. Transport Simulation in Microelectronics (1995), Birkhäuser, New York
97. Kersch A., Morokoff W.J., and Werner C. Selfconsistent simulation of sputter deposition with the Monte Carlo method. J. Appl. Phys. 75 (1994) 2278-2285
98. Knudsen M. Die Gesetze der molekular stromung und der inneren reibungstromung der gase durch röhren. Ann. Physik 28 (1909) 75-130
99. Knudsen M. The Kinetic Theory of Gases (1950), Methuen, Basel
100. Kogan M.N. Rarefied Gas Dynamics (1969), Plenum Press, London
101. Kogan M.N., Galkin V.S., and Fridlender O.G. Stresses produced in gases by temperature and concentration inhomogeneities. New type of free convection. Soviet Phys. Usp. 19 (1976) 420-438
102. Kot S.S., and Turcotte D.L. Beam-continuum model for hypersonic flow over a flat plate. AIAA J. 10 (1972) 291-295
103. Koura K. Comment on 'Direct Simulation scheme derived from the Boltzmann equation. I. Monocompo-nent gases'. J. Phys. Soc. Japan 50 (1981) 3829-3830
104. Koura K. Null-collision technique in the direct simulation Monte Carlo technique. Phys. Fluids 29 (1986) 3509-3511
105. Koura K. Null collision Monte Carlo method. Gas mixtures with internal degrees of freedom and chemical reactions. In: Muntz E.P., Weaver D.P., and Campbell D.H. (Eds). Rarefied Gas Dynamics: Physical Phenomena (1989), AIAA, New York 25-39
106. Koura K. Improved null-collision technique in the Direct Simulation Monte Carlo method: application to vibrational relaxation of nitrogen. Comput. Math. Appl. 35 (1998) 139-154
107. Koura K., and Matsumoto H. Variable soft sphere molecular model for inverse-power-law or Lennard-Jones potential. Phys. Fluids A 3 (1991) 2459-2465
108. AEC Report ORO-3588-1. Kuer I. Transport Theory Conference (1969), Blacksburgh, Washington
109. Kuer I. Reciprocity in scattering of gas molecules by surfaces. Surface Sci. 25 (1971) 225-237
110. Kuer I. Phenomenological aspects of gas-surface interaction. In: Cohen E.G.D., and Fiszdon W. (Eds). Fundamental Problems in Statistical Mechanics (1978), Ossolineum, VA 441-4167
111. Kuer I. Models of energy exchange in polyatomic gases. Operator Theory: Advances and Applications (1991), Birkhäuser, Warsaw 180-188
112. Kuer I., Moina J., and Krizanic F. The Knudsen model of thermal accommodation. In: Dini D., et al. (Ed). Rarefied Gas Dynamics (1974), Editrice Tecnico-Scientinca, Basel 97-108
113. Lecture Notes in Phys. Lanford, III O. The evolution of large classical systems. In: Moser J. (Ed). Dynamical Systems, Theory and Applications (1975), Springer, Pisa 1-111
114. Lebowitz J.L., Frisch H.L., and Helfand E. Nonequilibrium distribution functions in a fluid. Phys. Fluids 3 (1960) 325-338
115. Legge H. Experiments on a 70 degree blunted cone in rarefied hypersonic wind tunnel flow. AIAA Paper 95 (1995) 2140
116. Legge H. Force and heat transfer on a delta wing in rarefied flow. Workshop on Hypersonic Flows for Reentry Problems, Part II (1991), Antibes, Berlin
117. Lord R.G. Some extensions to the Cercignani-Lampis gas scattering kernel. Phys. Fluids A 3 (1991) 706-710
118. Lordi J.A., and Mates R.E. Rotational relaxation in nonpolar diatomic gases. Phys. Fluids 13 (1970) 291-308
119. Lorentz H.A. Über das Gleichgewicht der lebendingen Kraft unter Gasmolekülen. Sitzungsber. Akad. Wiss. 95 (1887) 115-152
120. Majda A. Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Appl. Math. Ser. Vol. 53 (1984), Springer, France
121. Maxwell J.C. On stresses in rarified gases arising from inequalities of temperature. Philos. Trans. Roy. Soc. 170 (1879) 231-256
122. Mc Court F.R.W., Beenakker J.J.M., Köhler W.E., and Kuer I. Nonequilibrium Phenomena in Polyatomic Gases (1990), Clarendon Press
123. McCroskey W.J., Bogdonoff S.M., and McDougall J.G. An experimental model for sharp flat plate in rarefied hypersonic flow. AIAA J. 4 (1966) 1580-1587
124. Messiter A.F. Boundary-layer flow near the trailing edge of a flat plate. SIAM J. Appl. Math. 18 (1970) 241-257
125. Metcalf S.C., Lillicrap D.C., and Berry C.J. A study of the effect of surface temperature on the shock-layer development over sharp-edged shapes in low-Reynolds-number high speed flow. In: Trilling L., and Wachman H.Y. (Eds). Rarefied Gas Dynamics (1969), Academic Press, Oxford 619-638
126. Millikan R.A. The general law of fall of a small spherical body through a gas, and its bearing upon the nature of molecular reflection from surfaces. Phys. Rev. 22 (1923) 1-23
127. Morse T.F. Kinetic model equations in a fluid. Phys. Fluids 7 (1964) 2012-2013
128. Moss J.N., and Bird G.A. Direct simulation of transitional flow for hypersonic re-entry conditions. Progr. in Astro, and Aero. 96 (1985) 113
129. Moss J.N., Chun C.H., and Price J.M. Hypersonic rarefied flow about a compression corner - DSMC simulation and experiment. AIAA Paper 91 (1991) 1313
130. Moss J.N., Dogra V.K., and Price J.M. DSMC simulation of viscous interactions for a hollow cylinder-flare configuration. AIAA Paper 94 (1994) 2015
131. Moss J.N., Price J.M., Dogra V.K., and Hash D.B. Comparison of DSMC and experimental results for hypersonic external flow. AIAA Paper 95 (1995) 2028
132. Muckenfuss C., and Curtiss C.E. Kinetic theory of nonspherical molecules. III. J. Chem. Phys. 29 (1958) 1257-1277
133. Nanbu K. Direct simulation scheme derived from the Boltzmann equation. J. Phys. Soc. Japan 49 (1980) 2042-2049
134. Nanbu K. Reply to a comment on 'Direct Simulation scheme derived from the Boltzmann equation. I. Monocomponent gases'. J. Phys. Soc. Japan 50 (1981) 3831-3832
135. Nocilla S. On the interaction between stream and body in free-molecule flow. In: Talbot L. (Ed). Rarefied Gas Dynamics (1961), Academic Press, New York 169-208
136. Nordsiek A., and Hicks B. Monte Carlo evaluation of the Boltzmann collision integral. In: Brundin C.L. (Ed). Rarefied Gas Dynamics (1967), Academic Press, New York 695-710
137. Oguchi H. The sharp leading edge problem in hypersonic flow. In: Talbot L. (Ed). Rarefied Gas Dynamics (1961), Academic Press, New York 501-524
138. Ohwada T., and Sone Y. Analysis of thermal stress slip flow and negative thermophoresis using the Boltzmann equation for hard-sphere molecules. Eur. J. Mech. B. 11 (1992) 389-414
139. Ohwada T., Sone Y., and Aoki K. Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard-sphere molecu. Phys. Fluids A 1 (1989) 2042-2049
140. Ohwada T., Sone Y., and Aoki K. Erratum. Phys Fluids A 2 (1990) 639
141. Pham-Van-Diep G.C., Erwin D.A., and Muntz E.P. Nonequilibrium molecular motion in a hypersonic shock wave. Science 245 (1989) 624-626
142. 4 between 11 and 300 K. Physica 64 (1973) 278-288
143. Pulvirenti M., Wagner W., and Zavelani M.B. Convergence of particle schemes for the Boltzmann equation. Eur. J. Mech. B. 7 (1994) 339-351
144. Rault D.F.G. Aerodynamics of the Shuttle Orbiter at high altitudes. J. Spacecraft and Rockets 31 (1994) 944-952
145. Reichelman D., and Nanbu K. Monte Carlo direct simulation of the Taylor instability in a rarefied gas. Phys. Fluids A 5 (1993) 2585-2587
146. Rudman S., and Rubin S.G. Hypersonic viscous flow over slender bodies with sharp leading-edges. AIAA J. 6 (1968) 1883-1890
147. 2 and HT. J. Chem. Phys. 47 (1967) 2621-2630
148. Schmidt B. Electron beam density measurements in shock waves in argon. J. Fluid Mech. 39 (1970) 361-373
149. Shorenstein M., and Probstein R.F. The hypersonic leading-edge problem. AIAA J. 6 (1968) 1898-1902
150. Siegel R., and Howell J.R. Thermal Radiation Heat Transfer (1992), Hemisphere Publishing, New York
151. Simmons R.S., and Lord R.G. Application of the C-L model to vibrational transitions of diatomic molecules during DSMC gas-surface interaction. In: Harvey J., and Lord G. (Eds). Rarefied Gas Dynamics (1995), Oxford Univ. Press, Washington 906-912
152. Sirovich L. Kinetic modeling of gas mixtures. Phys. Fluids 5 (1962) 908-918
153. Snider R.F. Quantum-mechanical modified Boltzmann equation for degenerate internal states. J. Chem. Phys. 32 (1960) 1051-1060
154. Sone Y. Flow induced by thermal stress in rarefied gas. Phys. Fluids 15 (1972) 1418-1423
155. Sone Y. Asymptotic theory of flow of rarefied gas over a smooth boundary I. In: Dini D., et al. (Ed). Rarefied Gas Dynamics (1974), Editrice Tecnico-Scientifica, Oxford 243-253
156. Sone Y., Aoki K., Tanaka S., Sugimoto H., and Bobylev A.V. Inappropriateness of the heat-conduction equation for the description of a temperature field of a stationary gas in the continuum limit: examination by asympt. Phys. Fluids A 8 (1996) 628-638
157. Stefanov S., and Cercignani C. Monte Carlo Simulation of Bénard's instability in a rarefied gas. Eur. J. Mech. B. 11 (1992) 543-553
158. Stefanov S., and Cercignani C. Monte Carlo simulation of the Taylor-Couette flow of a rarefied gas. J. Fluid Mech. 256 (1993) 199-213
159. Stefanov S., and Cercignani C. Monte Carlo Simulation of a channel flow of a rarefied gas. Eur. J. Mech. B. 13 (1994) 93-114
160. Stefanov S., and Cercignani C. Taylor-Couette flow of a rarefied gas. Proceedings of the International Symposium on Aerospace and Fluid Science (1994), Institute of Fluid Science, Tohoku University, Pisa 490-500
161. Cépaduès éditions. Stefanov S., Roussinov V., Cercignani C., Giurin M.C., and Struckmeier J. Rayleigh-Bénard chaotic convection of a rarefied gas. Toulouse. In: Brun R., Campargue R., Gatignol R., and Lengrand J.-C. (Eds). Rarefied Gas Dynamics (1999) 687-694
162. Stewartson K.O. On the flow near trailing edge of a flat plate. II. Mathematika 16 1 (1969) 106-121
163. Takata S., and Sone Y. Flow induced around a sphere with a nonuniform surface temperature in a rarefied gas, with application to the drag and thermal force problems of a spherical p. Eur. J. Mech. B. 14 (1995) 487-518
164. submitted to. Tanaka S., Aoki K., and Cercignani C. The velocity distribution function in an infinitely strong shock wave. Phys. Fluids (2000)
165. Tcheremissine F.G. Numerical methods for the direct solution of the kinetic Boltzmann equation. U.S.S.R. Comput. Math. Math. Phys. 25 (1985) 156-166
166. Tcheremissine F.G. Advancement of the method of direct numerical solving of the Boltzmann equation. In: Muntz E.P., Weaver D.P., and Campbell D.H. (Eds). Rarefied Gas Dynamics: Theoretical and Computational Techniques (1989), AIAA, Sendai 343-358
167. Tolman R.C. The Principles of Statistical Mechanics (1938), Clarendon Press, Washington
168. Uhlenbeck G.E. The Boltzmann Equation. Theory and Application. In: Cohen E.G.D., and Thirring W. (Eds) (1973), Springer, Oxford 107-119
169. Vogenitz F.W., Broadwell J.E., and Bird G.A. Leading-edge flow by the Monte Carlo direct simulation method. AIAA J. 8 (1972) 504-510
170. Wagner W. A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation. J. Statist. Phys. 66 (1992) 1011-1044
171. Waldmann L. Transporterscheinungen in Gasen von mittlerem Druck. In: Flügge S. (Ed). Handbuch der Physik (1958), Springer, Vienna 484-514
172. Waldmann L. The Boltzmann Equation. Theory and Application. In: Cohen E.G.D., and Thirring W. (Eds) (1973), Springer, Berlin 223-246
173. Part c. Wang Chang C.S., and Uhlenbeck G.E. Studies in Statistical Mechanics. In: de Boer J., and Uhlenbeck G.E. (Eds) (1964), North-Holland, Vienna
174. Welander P. On the temperature jump in a rarefied gas. Arkiv Fysik 7 (1954) 507-553
175. Williams M.M.R. A phenomenological study of gas-surface interactions. J. Phys. D. Appl. Phys. 4 (1971) 1315-1319
176. Williams M.M.R., and Loyalka S.K. Aerosol Science. Theory & Practice (1991), Pergamon Press, Amsterdam
177. Woronowicz M.S., and Rault D.F.G. Cercignani-Lampis-Lord gas-surface interaction model: comparison between theory and simulation. J. Spacecraft and Rockets 31 (1994) 532-534
178. Yen S.M., Hicks B., and Osteen R.M. Further development of a Monte Carlo method for the evaluation of Boltzmann collision integral. In: Becker M., and Fiebig M. (Eds). Rarefied Gas Dynamics (1974), DFVLR-Press, Oxford 1-10
179. Yoshizawa Y. Wave structures of a chemically reacting gas by the kinetic theory of gases. In: Potter J.L. (Ed). Rarefied Gas Dynamics, Part I (1977), AIAA, Porz-Wahn 501-517