Some exact numerical results for the BGK model: Couette, Poiseuille and thermal creep flow between parallel plates

Numerically “exact” results for the Couette flow, Poiseuille flow and thermal creep flow between parallel plates are given for the BGK model. Equations obtained earlier by Cercignani and Williams, who used the method of elementary solutions, are solved by convergent Liouville-Series and results are compared with works of other authors.ZusammenfassungNumerisch “exakte” Lösungen für die Couette-, Poiseuille- und thermische Kriechströmung zwischen parallelen Platten werden nach dem BGK-Modell angegeben. Die früheren Gleichungen von Cercignani und Williams, die die Methoden der elementaren Lösungen benutzt haben, werden durch konvergierende Liouville-Reihen gelöst. Die Ergebnisse werden mit Arbeiten anderer Verfasser verglichen.

[1]  G. C. Pomraning,et al.  Linear Transport Theory , 1967 .

[2]  J. Ferziger Flow of a Rarefied Gas through a Cylindrical Tube , 1967 .

[3]  Q/sub n/ and F/sub n/ integrals for the BGK model , 1975 .

[4]  S. Loyalka,et al.  Thermal Creep Slip with Arbitrary Accommodation at the Surface , 1971 .

[5]  S. Loyalka,et al.  An Exact Expression for the Diffusion Slip Velocity in a Binary Gas Mixture , 1970 .

[6]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[7]  Carlo Cercignani,et al.  Variational Approach to Boundary‐Value Problems in Kinetic Theory , 1966 .

[8]  J. T. Kriese,et al.  Elementary solutions of coupled model equations in the kinetic theory of gases , 1974 .

[9]  Kenneth M. Case,et al.  Elementary solutions of the transport equation and their applications , 1960 .

[10]  S. Loyalka Kinetic Theory of Thermal Transpiration and Mechanocaloric Effect. I , 1971 .

[11]  Mikhail Naumovich Kogan,et al.  Rarefied Gas Dynamics , 1969 .

[12]  J. R. Thomas,et al.  Half‐space problems in the kinetic theory of gases , 1973 .

[13]  A. Stroud,et al.  Nodes and Weights of Quadrature Formulas , 1965 .

[14]  Carlo Cercignani,et al.  Elementary solutions of the linearized gas-dynamics boltzmann equation and their application to the slip-flow problem , 1962 .

[15]  S. Loyalka Thermal Transpiration in a Cylindrical Tube , 1969 .

[16]  J. Ferziger,et al.  Model Dependence of the Slip Coefficient , 1967 .

[17]  S. K. Loyalka,et al.  Some numerical results for the BGK model: Thermal creep and viscous slip problems with arbitrary accomodation at the surface , 1975 .

[18]  D. Willis Comparison of Kinetic Theory Analyses of Linearized Couette Flow , 1962 .

[19]  J. R. Thomas,et al.  Temperature‐jump problem with arbitrary accommodation , 1978 .

[20]  C. Cercignani Plane Couette flow according to the method of elementary solutions , 1965 .

[21]  C. Cercignani The Kramers problem for a not completely diffusing wall , 1965 .

[22]  M. Williams Rarefied gas flow between parallel plates , 1969, Mathematical Proceedings of the Cambridge Philosophical Society.

[23]  Some applications of a linearized kinetic model with correct prandtl number , 1966 .

[24]  W. Strieder Upper and Lower Bounds on the Shear Stress of a Rarefied Gas , 1970 .