A linearization of Mieussens's discrete velocity model for kinetic equations

European Journal of Mechanics, B/Fluids

Volumn 26, Issue 2, 2007, Pages 182-192

  Zheng, Yingsong ^a   Struchtrup, Henning ^b  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Couette flow; Discrete velocity model; Kinetic equation; Rarefied gas dynamics; Shock waves

Indexed keywords

COMPUTATIONAL COMPLEXITY; GAS DYNAMICS; LINEARIZATION; SHOCK WAVES;

BOLTZMANN-BGK EQUATION; KINETIC EQUATIONS; MIEUSSENS'S DISCRETE VELOCITY MODEL; STATIONARY PLANAR COUETTE FLOW; VELOCITY-DEPENDENT COLLISION FREQUENCY;

VELOCITY MEASUREMENT;

EID: 33846189410     PISSN: 09977546     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechflu.2006.08.003     Document Type: Article

References (26)

1. Struchtrup H. Macroscopic Transport Equations for Rarefied Gas Flows-Approximation Methods in Kinetic Theory. Interaction of Mechanics and Mathematics Series (2005), Springer, Heidelberg
2. Kogan M.N. Rarefied Gas Dynamics (1969), Plenum Press
3. Cercignani C. Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations (2000), Cambridge University Press
4. Garzo V., and Santos A. Kinetic Theory of Gases in Shear Flows (2003), Kluwer Academic Publishers, Dordrecht
5. Y. Zheng, Analysis of kinetic models and macroscopic continuum equations for rarefied gas dynamics, Ph.D. thesis, Dept. Mech. Eng., Univ. of Victoria, Canada, 2004
6. Mieussens L. Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries. J. Comput. Phys. 162 (2000) 429-466
7. Mieussens L. Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics. Math. Models Methods Appl. Sci. 10 (2000) 1121-1149
8. Mieussens L. Convergence of a discrete-velocity model for the Boltzmann-BGK equation. Comput. Math. Appl. 41 (2001) 83-96
9. Mieussens L., and Struchtrup H. Numerical comparison of BGK-models with proper Prandtl number. Phys. Fluids 16 (2004) 2797-2813
10. Zheng Y., and Struchtrup H. Ellipsoidal statistical BGK model with velocity-dependent collision frequency. Phys. Fluids 17 (2005) 127103 (1-17)
11. Bhatnagar P.L., Gross E.P., and Krook M. A model for collision processes in gases. I: small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94 (1954) 511-525
12. Lowell J., and Holway H. New statistical models for kinetic theory: methods of construction. Phys. Fluids 9 (1966) 1658-1673
13. Andries P., and Perthame B. The ES-BGK model equation with correct Prandtl number. AIP Conf. Proc. vol. 585 (2001) 30-36
14. Zheng Y., and Struchtrup H. Burnett equations for the ellipsoidal statistical BGK model. Continuum Mech. Thermodyn. 16 (2004) 97-108
15. Struchtrup H. The BGK-model with velocity-dependent collision frequency. Continuum Mech. Thermodyn. 9 (1997) 23-31
16. Bouchut F., and Perthame B. A BGK model for small Prandtl number in the Navier-Stokes approximation. J. Stat. Phys. 71 (1993) 191-207
17. Barichello L.B., Bartz A.C.R., Camargo M., and Siewert C.E. The temperature-jump problem for a variable collision frequency model. Phys. Fluids 14 (2002) 382-391
18. Cercignani C. The method of elementary solutions for kinetic models with velocity-dependent collision frequency. Ann. Phys. 40 (1966) 469-481
19. Cercignani C. Knudsen layers: theory and experiment. In: Muller U., Rosner K.G., and Schmidt B. (Eds). Recent Developments in Theoretical and Experimental Fluid Mechanics (1979), Springer-Verlag, Berlin 187-195
20. Yee H.C. Construction of explicit and implicit symmetric TVD schemes and their applications. J. Comput. Phys. 68 (1987) 151-179
21. Press W.H., Flannery B.P., Teukolsky S.A., and Vetterling W.T. Numerical Recipes (1986), Cambridge University Press
22. Dennis J.E., and Schnabel R.B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations (1983), Prentice-Hall
23. L. Mieussens (Toulouse, France), private communication, 2003
24. Pham-Van-Diep G.C., Erwin D.A., and Muntz E.P. Testing continuum descriptions of low-Mach-number shock structures. J. Fluid Mech. 232 (1991) 403-413
25. A. Schuetze, Direct simulation by Monte Carlo modeling Couette flow using dsmc1as.f: A user's manual, Technical Report, Dept. Mech. Eng., Univ. of Victoria, Canada, 2003
26. Bird R.B., Stewart W.E., and Lightfoot E.N. Transport Phenomena. second ed. (2002), John Wiley & Sons