Stable transport equations for rarefied gases at high orders in the Knudsen number

Physics of Fluids

Volumn 16, Issue 11, 2004, Pages 3921-3934

  Struchtrup, Henning ^a  

^a UNIVERSITY OF VICTORIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; KINETIC THEORY; NAVIER STOKES EQUATIONS;

BOLTZMAN EQUATION; PHASE DENSITY; RAREFIED GASES;

GASES;

PHYSICS;

EID: 8844265401     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1782751     Document Type: Article

References (32)

1. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge, 1970).
2. C. Cercignani, Theory and Application of the Boltzmann Equation (Scottish Academic, Edinburgh, 1975).
3. J. H. Ferziger and H. G. Kaper, Mathematical Theory of Transport Processes in Gases (North-Holland, Amsterdam, 1972).
4. M. S. Shavaliyev, "Super-Burnett corrections to the stress tensor and the heat flux in a gas of Maxwellian molecules," J. Appl. Math. Mech. 57, 573 (1993).
5. A. V. Bobylev, "The Chapman-Enskog and Grad methods for solving the Boltzmann equation," Sov. Phys. Dokl. 27, 29 (1982).
6. H. Struchtrup, "Failures of the Burnett and Super-Burnett equations in steady state processes," Continuum Mech. Thermodyn. (in press).
7. M. Torrilhon and H. Struchtrup, "Regularized 13-moment-equations: shock structure calculations and comparison to Burnett models," J. Fluid Mech. 513, 171 (2004)
8. X. Zhong, R. W. MacCormack, and D. R. Chapman, "Stabilization of the Burnett equations and applications to high-altitude hypersonic flows," AIAA Pap. 91-0770 (1991).
9. X. Zhong, R. W. MacCormack, and D. R. Chapman, "Stabilization of the Burnett equations and applications to hypersonic flows," AIAA J. 31, 1036 (1993).
10. S. Jin and M. Slemrod, "Regularization of the Burnett equations via relaxation," J. Stat. Phys. 103, 1009 (2001).
11. S. Jin, L. Pareschi, and M. Slemrod, "A relaxation scheme for solving the Boltzmann equation based on the Chapman-Enskog expansion," Acta Math. Appl. Sin. 18, 37 (2002).
12. H. Grad, "On the kinetic theory of rarefied gases," Commun. Pure Appl. Math. 2, 325 (1949).
13. H. Grad, "Principles of the kinetic theory of gases," in Handbuch der Physik, edited by S. Flügge (Springer, Berlin, 1958), Vol. 12.
14. I. Müller and T. Ruggeri, Rational Extended Thermodynamics, in Springer Tracts in Natural Philosophy Vol. 37, edited by C. Truesdell (Springer, New York, 1998).
15. W. Weiss, "Continuous shock structure in extended thermodynamics," Phys. Rev. E 52, 5760 (1995).
16. S. Reinecke and G. M. Kremer, "Method of moments of grad," Phys. Rev. A 42, 815 (1990).
17. S. Reinecke and G. M. Kremer, "Burnett's equations from a (13+9N)-field theory," Continuum Mech. Thermodyn. 8, 121 (1996).
18. H. Struchtrup, Some Remarks on the Equations of Burnett and Grad, in Transport in Transition Regimes Vol. 135 (Springer, New York. 2003).
19. H. Struchtrup and M. Torrilhon, "Regularization of Grad's 13 moment equations: Derivation and linear analysis," Phys. Fluids 15 2668 (2003).
20. I. V. Karlin, A. N. Gorban, G. Dukek, and T. F. Nonnenmacher, "Dynamic correction to moment approximations," Phys. Rev. E 57, 1668 (1998).
21. I. Müller, D. Reitebuch, and W. Weiss, "Extended thermodynamics - consistent in order of magnitude," Continuum Mech. Thermodyn. 15, 113 (2003).
22. P. L. Bhatnagar, E. P. Gross, and M. Krook, "A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems," Phys. Rev. 94, 511 (1954).
23. C. Truesdell and R. G. Muncaster, Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas (Academic, New York, 1980).
24. H. Struchtrup, "Zur irreversiblen Thermodynamik der Strahlung," Dissertation, Technical University, Berlin, 1996.
25. L. Waldmann "Transporterscheinungen in Gasen von mittlerem Druck," Handbuch der Physik XII: Thermodynamik der Gase, edited by S. Flügge (Springer, Berlin, 1958).
26. M. Torrihon, J. D. Au, and H. Struchtrup, "Explicit fluxes and productions for large systems of the moment method based on extended thermodynamics," Continuum Mech. Thermodyn. 15, 97 (2003).
27. K. A. Fiscko and D. R. Chapman, "Comparison of Burnett, Super-Burriett and Monte Carlo solutions for hypersonic shock structure," in Proceedings of the 16th Symposium on Rarefied Gasdynamics, edited by R Muntz (AIAA, Washington, 1989) pp. 374-395.
28. E. A. Spiegel and J.-L. Thiffeault, "Higher-order continuum approximation for rarefied gases," Phys. Fluids 15, 3558 (2003).
29. I. V. Karlin and A. N. Gorban, "Hydrodynamics from Grad's equations: What can we learn from exact solutions?" Ann. Phys. (Leipzig) 11, 783 (2002).
30. H. Struchtrup, "Heat transfer in the transition regime: Solution of boundary value problems for Grad's moment equations via kinetic schemes," Phys. Rev. E 65, 041204 (2002).
31. W. Dreyer and H. Struchtrup, "Heat pulse experiments revisited," Continuum Mech. Thermodyn. 5, 3 (1993).
32. H. Struchtrup, "Derivation of 13 moment equations for rarefied gas flow to second order accuracy for arbitrary interaction potentials," Multiscale Model. Simul. (in press).