The temperature-jump problem in rarefied-gas dynamics

An analytical version of the discrete-ordinates method is used here to solve the classical temperature-jump problem based on the BGK model in rarefied-gas dynamics. In addition to a complete development of the discrete-ordinates method for the application considered, the computational algorithm is implemented to yield very accurate results for the temperature jump and the complete temperature and density distributions in the gas. The algorithm is easy to use, and the developed code runs typically in less than a second on a 400 MHz Pentium-based PC.

[1]  J. R. Thomas The FN-method in kinetic theory I. Half-space problems , 1985 .

[2]  M. M. R. Williams,et al.  A review of the rarefied gas dynamics theory associated with some classical problems in flow and heat transfer , 2001 .

[3]  Brian T. Smith,et al.  Matrix Eigensystem Routines — EISPACK Guide , 1974, Lecture Notes in Computer Science.

[4]  Y. Pao Temperature and Density Jumps in the Kinetic Theory of Gases and Vapors , 1971 .

[5]  P. Welander,et al.  ON THE TEMPERATURE JUMP IN A RAREFIED GAS , 1954 .

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

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

[8]  Felix Sharipov,et al.  Data on Internal Rarefied Gas Flows , 1998 .

[9]  B. S. Garbow,et al.  Matrix Eigensystem Routines — EISPACK Guide , 1974, Lecture Notes in Computer Science.

[10]  V. Klema LINPACK user's guide , 1980 .

[11]  C. E. Siewert,et al.  A discrete-ordinates solution for a non-grey model with complete frequency redistribution , 1999 .

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

[13]  C. Siewert,et al.  A discrete-ordinates solution for Poiseuille flow in a plane channel , 1999 .

[14]  C. E. Siewert,et al.  Unified solutions to classical flow problems based on the BGK model , 2001 .

[15]  Y. Onishi KINETIC THEORY ANALYSIS FOR TEMPERATURE AND DENSITY FIELDS OF A SLIGHTLY RAREFIED BINARY GAS MIXTURE OVER A SOLID WALL , 1997 .

[16]  Carlo Cercignani,et al.  Half-space problems in the kinetic theory of gases , 1986 .

[17]  Carlo Cercignani,et al.  Mathematical Methods in Kinetic Theory , 1970 .

[18]  G. Rybicki Radiative transfer , 2019, Climate Change and Terrestrial Ecosystem Modeling.

[19]  C. Siewert A Discrete-Ordinates Solution for Heat Transfer in a Plane Channel , 1999 .

[20]  M. M. R. Williams,et al.  Mathematical methods in particle transport theory , 1971 .

[21]  C. Cercignani The Boltzmann equation and its applications , 1988 .