A renormalization method for the Chapman-Enskog expansion

Physica D: Nonlinear Phenomena

Volumn 109, Issue 3-4, 1997, Pages 257-273

  Slemrod, M ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Boltzmann equation; Burnett equation; Chapman Enskog expansion; Stability

Indexed keywords

EID: 0000674820     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)00068-7     Document Type: Article

References (15)

1. A.V. Bobylev, The Chapman-Enskog and Grad methods for solving the Boltzmann equation, Soviet Phys. Dokl. 27 (1) 1982.
2. H. Brezis, Analyse Fonctionelle, Théorie et Applications (Masson, Paris, 1987).
3. C. Cercignani, The Boltzmann Equation and its Applications (Springer, New York, 1988).
4. G.-Q. Chen, C.D. Levermore and T.-P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Commun. Pure Appl. Math. 47 (1994) 787-830.
5. K.A. Fiscko and D.R. Chapman, Hypersonic shock structure with Burnett terms in the viscous stress and heat flux, AIAA 88-2733, in: Proc. American Institute of Aeronautics and Astronautics Thermophysics, Plasmadynamics, and Lasers Conf. (1988).
6. K.A. Fiscko and D.R. Chapman, Comparison of Burnett, Super-Burnett and Monte Carlo Solutions for Hypersonic Shock Structure, in: Proc. 16th Int. Symp. Rarefied Gas Dynamics (1988) pp. 374-395.
7. T.D. Foch, On the higher order hydrodynamic theories of shock structure, Acta Phys. Austriaca, Suppl. X (1973) 123-140.
8. G.B. Folland, Introduction to Partial Differential Equations, 2nd Ed. (Princeton University Press, Princeton, 1995).
9. H. Grad, Asymptotic theory of the Boltzmann equation, Phys. Fluids 6 (1963) 147-181.
10. E. Hille and R.H. Phillips, Functional Analysis and Semi-groups, American Mathematical Society Colloquium Publication, Vol. 31 (AMS, Providence, RI, 1957).
11. P. Rosenau, Extending hydrodynamics via the regularization of the Chapman-Enskog expansion, Phys. Rev. A 40 (12) (1989) 7193-7196.
12. C. Truesdell and R.G. Muncaster, Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas (Academic Press, New York, 1980).
13. C. Truesdell and W. Noll, in: The Nonlinear Field Theories of Mechanics, Encyclopedia of Physics, ed. S. Flugge, Vol. III (3) (Springer, New York).
14. L.C. Woods, Transport processes in dilute gases over the whole range of Knudsen numbers. Part 1: General theory, J. Fluid Mech. 93 (3) (1979) 585-607.
15. X. Zhang, R.W. Mac Cormack and D.R. Chapman, Stabilization of the Burnett equation and application to high altitude hypersonic flows, AIAA-91-0770, in: Proc. American Institute of Aeronautics and Astronautics Thermophysics, Plasmadynamics, and Lasers Conf. (1991).