Shock-wave structure for a binary gas mixture: finite-difference analysis of the Boltzmann equation for hard-sphere molecules

European Journal of Mechanics, B/Fluids

Volumn 20, Issue 1, 2001, Pages 87-126

  Kosuge, Shingo ^a   Aoki, Kazuo ^a   Takata, Shigeru ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BINARY MIXTURES; FINITE DIFFERENCE METHOD; MOLECULES; VELOCITY;

BINARY GAS MIXTURE; BOLTZMANN EQUATION; HARD SPHERE MOLECULES; NUMERICAL KERNEL METHOD;

SHOCK WAVES;

EID: 0035078962     PISSN: 09977546     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0997-7546(00)00133-3     Document Type: Article

References (39)

1. Mott-Smith H.M., The solution of the Boltzmann equation for a shock wave, Phys. Rev. 2nd Ser. 82 (1951) 885.
2. Liepmann H.W., Narashimha R., Chahine M.T., Structure of a plane shock layer, Phys. Fluids 5 (1962) 1313.
3. Bird G.A., Aspects of the structure of strong shock waves, Phys. Fluids 13 (1970) 1172.
4. Cercignani C., The Boltzmann Equation and Its Applications, Chap. VII, Springer, Berlin, 1988.
5. Fiszdon W., The structure of plane shock waves, in: Fiszdon W. (Ed.), Rarefied Gas Flows: Theory and Experiment, Springer, Vienna, 1981, p. 447.
6. Bird G.A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford Univ. Press, Oxford, 1994.
7. Cercignani C., Frezzotti A., Grosfils P., The structure of an infinitely strong shock wave, Phys. Fluids 11 (1999) 2757.
8. Ohwada T., Structure of normal shock waves: Direct numerical analysis of the Boltzmann equation for hard-sphere molecules, Phys. Fluids A 5 (1993) 217.
9. Sone Y., Ohwada T., Aoki K., Temperature jump and Knudsen layer in a rarefied gas over a plane wall: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules, Phys. Fluids A 1 (1989) 363.
10. Ohwada T., Sone Y., Aoki K., Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard-sphere molecules, Phys. Fluids A 1 (1989) 1588.
11. Ohwada T., Sone Y., Analysis of thermal stress slip flow and negative thermophoresis using the Boltzmann equation for hard-sphere molecules, Eur. J. Mech. B-Fluids 11 (1992) 389.
12. Ohwada T., Sone Y., 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 molecules, Phys. Fluids A 1 (1989) 2042.
13. Sone Y., Takata S., Ohwada T., Numerical analysis of the plane Couette flow of a rarefied gas on the basis of the linearized Boltzmann equation for hard-sphere molecules, Eur. J. Mech. B-Fluids 9 (1990) 273.
14. Takata S., Sone Y., Aoki K., Numerical analysis of a uniform flow of a rarefied gas past a sphere on the basis of the Boltzmann equation for hard-sphere molecules, Phys. Fluids A 5 (1993) 71 6.
15. Sone Y., Takata S., Wakabayashi M., Numerical analysis of a rarefied gas flow past a volatile particle using the Boltzmann equation for hard-sphere molecules, Phys. Fluids 6 (1994) 1914.
16. Takata S., Sone Y., Flow induced around a sphere with a non-uniform surface temperature in a rarefied gas, with application to the drag and thermal force problems of a spherical particle with an arbitrary thermal conductivity, Eur. J. Mech. B-Fluids 14 (1995) 487.
17. Ohwada T., Numerical analysis of normal shock waves on the basis of the Boltzmann equation for hard-sphere molecules, in: Shizgal B.D., Weaver D.P. (Eds.), Rarefied Gas Dynamics: Theory and Simulations, AIAA, Washington, D.C., 1994, p. 482.
18. Ohwada T., Heat flow and temperature and density distributions in a rarefied gas between parallel plates with different temperatures: Finite difference analysis of the nonlinear Boltzmann equation for hard-sphere molecules, Phys. Fluids 8 (1996) 2153.
19. Ohwada T., Investigation of heat transfer problem of a rarefied gas between parallel plates with different temperatures, in: Shen C. (Ed.), Rarefied Gas Dynamics, Peking University Press, Beijing, 1997, p. 327.
20. Center R.E., Measurement of shock-wave structure in Helium-Argon mixtures, Phys. Fluids 10 (1967) 1777.
21. Harnett L.N., Muntz E.P., Experimental investigation of normal shock wave velocity distribution functions in mixtures of Argon and Helium, Phys. Fluids 15 (1972) 565.
22. Gmurczyk A.S., Tarczyński M., Walenta Z.A., Shock wave structure in the binary mixtures of gases with disparate molecular masses, in: Campargue R. (Ed.), Rarefied Gas Dynamics, Commissariat a L'energie Atomique, Paris, Vol. 1, 1979, p. 333.
23. Oberai M.M., A Mott-Smith distribution to describe the structure of a plane shock wave in a binary mixture, Phys. Fluids 9 (1966) 1634.
24. Oberai M.M., Sinha U.N., Shock wave structure in binary gas mixture, in: Becker M., Fiebig M. (Eds.), Rarefied Gas Dynamics, DFVLR, Povz-Wahn, Vol. 1, 1974, B. 25.
25. Beylich A.E., Kinetic model for the shock structure in a binary gas mixture, Phys. Fluids 11 (1968) 2764.
26. Fernández-Feria R., Fernández de la Mora J., Shock wave structure in gas mixtures with large mass disparity, J. Fluid Mech. 179 (1987) 21.
27. Abe K., Oguchi H., Shock wave structures in binary gas mixtures with regard to temperature overshoot, Phys. Fluids 17 (1974) 1333.
28. Hamel B.B., Disparate mass mixture flows, in: Potter J.L. (Ed.), Rarefied Gas Dynamics, AIAA, New York, Vol. 1, 1977, p. 171.
29. Bird G.A., The structure of normal shock waves in a binary gas mixture, J. Fluid Mech. 31 (1968) 657.
30. Bird G.A., Shock wave structure in gas mixtures, in: Oguchi H. (Ed.), Rarefied Gas Dynamics, University of Tokyo Press, Tokyo, Vol. 1, 1984, p. 175.
31. Raines A.A., Conservative method of evaluation of Boltzmann collision integrals for cylindrical symmetry, in: Brun R., Campargue R., Gatignol R., Lengrand J.-C. (Eds.), Rarefied Gas Dynamics, Cépaduès-Éditions, Toulouse, Vol. 2, 1999, p. 173.
32. Kogan M.N., Rarefied Gas Dynamics, Plenum, New York, 1969.
33. Chapman S., Cowling T.G., The Mathematical Theory of Non-uniform Gases, 3rd Ed., Cambridge University Press, London, 1970.
34. Abramowitz M., Stegun I.A., Handbook of Mathematical Functions, Dover, New York, 1965, Chap. 22.
35. Ralston A., Rabinowitz P., A First Course in Numerical Analysis, 2nd Ed., McGraw-Hill, New York, 1978, Chap. 4.
36. Garzó V., Santos A., Brey J.J., A kinetic model for a multicomponent gas, Phys. Fluids A 1 (1989) 380.
37. Bobylev A.V., Palczewski A., Schneider J., A consistency result for a discrete velocity model of the Boltzmann equation, SIAM J. Numer. Anal. 34 (1997) 1865.
38. Rogier F., Schneider J., A direct method for solving the Boltzmann equation, Transp. Ther. Stat. Phys. 23 (1994) 313.
39. Panferov V., Heintz A., A new consistent discrete-velocity model for the Boltzmann equation, Math. Method. Appl. Sci. (2000) (accepted for publication).