Nine-moment phonon hydrodynamics based on the modified grad-type approach: Hyperbolicity of the one-dimensional flow

Journal of Physics A: Mathematical and General

Volumn 37, Issue 45, 2004, Pages 11053-11072

  Banach, Zbigniew ^a   Larecki, Wieslaw ^a  

^a INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 9944224576     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/45/021     Document Type: Article

References (32)

1. Peierls R E 1955 Quantum Theory of Solids (London: Oxford University Press)
2. Beck H 1975 Second sound and related thermal conduction phenomena Dynamical Properties of Solids vol 2 ed G K Horton and A A Maradudin (Amsterdam: North-Holland) p 205
3. Gurevich V L 1980 Kinetika Fononnykh Sistem (Moscow: Nauka)
4. Larecki W 1992 Nuovo Cimento D 14 141
5. Banach Z and Larecki W 2004 Nine-moment phonon hydrodynamics based on the modified Grad-type approach: formulation. J. Phys. A: Math. Gen. 37 9805
6. Banach Z and Piekarski S 1989 J. Math. Phys. 30 1826
7. Callaway J 1991 Quantum Theory of the Solid State (Boston, MA: Academic)
8. Jeffrey A 1976 Quasilinear Hyperbolic Systems and Waves (London: Pitman)
9. Majda A 1984 Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables (Berlin: Springer)
10. Smoller J 1983 Shock Waves and Reaction-Diffusion Equations (New York: Springer)
11. Larecki W 1997 Arch. Mech. 49 865
12. Larecki W 1998 Matrix analysis approach to determination of entropies for hyperbolic systems of conservation equations Trends in Continuum Physics ed B T Maruszewski, W Muschik and A Radowicz (Singapore: World Scientific) p 202
13. Taylor M E 1996 Partial Differential Equations. III. Nonlinear Equations (New York: Springer)
14. Friedrichs K O and Lax P D 1971 P roc. Natl Acad. Sci. USA 68 1686
15. Courant R and Hubert D 1962 Methods of Mathematical Physics vol II (New York: Interscience)
16. Dreyer W 1987 J. Phys. A: Math. Gen. 20 6505
17. Levermore C D 1996 J. Stat. Phys. 83 1021
18. Banach Z and Larecki W 2002 Rev. Math. Phys. 14 469
19. Banach Z 2003 Class. Quantum Grav. 20 1443
20. Grad H 1949 Commun. Pure Appl. Math. 2 331
21. Grad H 1958 Principles of the kinetic theory of gases Handbuch der Physik vol 12 ed S Flügge (Berlin: Springer) p 205
22. Banach Z and Piekarski S 1989 J. Math. Phys. 30 1816
23. Junk M 1998 J. Stat. Phys. 93 1143
24. Hoffman K and Kunze R 1961 Linear Algebra (Englewood Cliffs, NJ: Prentice-Hall)
25. Jameson A, Kreindler E and Lancaster P 1992 Linear Algebr. Appl. 160 189
26. Groth C P T, Gombosi T I, Roe P L and Brown S L 1994 Gaussian-based moment-method closures for the solution of the Boltzmann equation 5th Int. Conf. on Hyperbolic Problems (Stony Brook, NJ, June 1994)
27. Groth C P T, Roe P L, Gombosi T I and Brown S L 1995 On the nonstationary wave structure of a 35-moment closure for rarefied gas dynamics AlAA 26th Fluid Conf. (San Diego, CA, June 1995)
28. Struchtrup H and Weiss W 1998 Phys. Rev. Lett. 80 5048
29. Liu I S, Rincon M A and Müller I 2002 Continuum Mech. Thermodyn. 14 483
30. Brini F and Ruggeri T 2002 Continuum Mech. Thermodyn. 14 165
31. Brown S L 1996 Approximate Riemann solvers for moment models of dilute gases Dissertation University of Michigan
32. Müller I and Ruggeri T 1998 Rational Extended Thermodynamics (New York: Springer)