Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-18T22:35:26.606Z Has data issue: false hasContentIssue false

On the steady Krook kinetic equation: Part 1

Published online by Cambridge University Press:  28 March 2006

Donald G. Anderson
Affiliation:
Division of Engineering and Applied Physics, Harvard University, Cambridge, Massachusetts

Abstract

In this paper systems of non-linear integral equations are formulated which are equivalent to the Krook kinetic equation for steady problems in two and three space-dimensions. The boundary conditions used are discussed and some of the properties of the equations which are significant in their numerical solution pointed out. This work will then serve as a basis for the consideration of a sequence of particular problems to be presented in subsequent papers.

Type
Research Article
Copyright
© 1966 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, D. G. 1963 Numerical experiments in kinetic theory. Ph.D. Thesis, Harvard University, Cambridge, Massachusetts.
Anderson, D. G. 1965 Tech. Rep. no. 15, Engineering Sciences Laboratory, Harvard University, Cambridge, Massachusetts (to be published in J. Fluid Mech.).
Anderson, D. G. & Macomber, H. K. 1964 Tech. Rep. no. 10, Engineering Sciences Laboratory, Harvard University, Cambridge, Massacusetts (to be published in J. Math. & Phys.).
Anderson, D. G. & Macomber, H. K. 1965 In Proc. 4th Int. Symp. on Rarefied Gas Dynamics (ed. J. H. de Leeuw). New York: Academic Press.
Bienkowski, G. 1965 In Proc. 4th Int. Symp. on Rarefied Gas Dynamics (ed. J. H. de Leeuw). New York: Academic Press.
Brau, C. A. 1965 Models for collision processes in polyatomic gases, Ph.D. Thesis, Harvard University, Cambridge, Massachusetts.
Chahine, M.T. 1963 In Proc. 3rd Int. Symp. on Rarefied Gas Dynamics (ed. J. A. Laurmann). New York: Academic Press.
Chahine, M. T. & Narasimha, R. 1965 In Proc. 4th Int. Symp. on Rarefied Gas Dynamics (ed. J. H. de Leeuw). New York: Academic Press.
Chu, C. K. 1965 Phys. Fluids, 8, 12.
Fishman, F. G. 1957 A kinetic approach to neutral and ionized gas dynamics, Ph.D. Thesis, Harvard University, Cambridge, Massachusetts.
Krook, M. 1955 Phys. Rev. 99, 189.
Krook, M. 1959 J. Fluid Mech. 6, 52.
Leeuw De, J. H. (ed.) 1965 Proc. 4th Int. Symp. on Rarefied Gas Dynamics. New York: Academic Press.
Liepmann, H. W., Narasimha, R. & Chahine, M. T. 1962 Phys. Fluids, 5, 1313.
Macomber, H. K. 1965 Moment methods for non-linear problems in kinetic theory, Ph.D. Thesis, Harvard University, Cambridge Massachusetts. (Also available as Tech. Rep. no. 13, Engineering Sciences Laboratory, Harvard University, Cambridge, Massachusetts.)Google Scholar
Mccune, J. E., Morse, T. F. & Sandri, G. 1963 Proc. 3rd Int. Symp. on Rarefied Gas Dynamics, (ed. J. A. Laurmann). New York: Academic Press.
Mccune, J. E., Sandri, G. & Frieman, E. A. 1963 Proc. 3rd Int. Symp. on Rarefied Gas Dynamics (ed. J. A. Laurmann). New York: Academic Press.
Willis, D. R. 1960a Proc. 1st Int. Symp. on Rarefied Gas Dynamics (ed. F. M. Devienne). New York: Pergamon Press.
Willis, D. R. 1960b Tech. Note no. 4, Division of Gas Dynamics, Royal Institute of Technology, Stockholm, Sweden.
Willis, D. R. 1961 Proc. 2nd Int. Symp. on Rarefied Gas Dynamics, (ed. L. Talbot). New York: Academic Press.
Willis, D. R. 1962 Phys. Fluids, 5, 127.
Willis, D. R. 1963 Proc. 3rd Int. Symp. on Rarefied Gas Dynamics (ed. J. A. Laurmann New York: Academic Press.