Linear kinetic heat transfer: Moment equations, boundary conditions, and Knudsen layers

Physica A: Statistical Mechanics and its Applications

Volumn 387, Issue 8-9, 2008, Pages 1750-1766

  Struchtrup, H ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Asymptotic expansion; Knudsen layers; Rarefied flows

Indexed keywords

ASYMPTOTIC ANALYSIS; BOUNDARY CONDITIONS; ENERGY TRANSFER; EQUATIONS OF MOTION; KINETIC ENERGY; LINEAR EQUATIONS; PROBLEM SOLVING;

ASYMPTOTIC EXPANSION; KNUDSEN LAYERS; RAREFIED FLOWS;

HEAT TRANSFER;

EID: 38349061496     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2007.11.044     Document Type: Article

References (33)

1. Karniadakis G.E., Beskok A., and Aluru N. Microflows and Nanoflows: Fundamentals and Simulation (2005), Springer, New York
2. Cercignani C. Slow Rarefied Flows. Theory and Application to Micro-Electro-Mechanical Systems (2006), Birkhäuser, Basel
3. Chapman S., and Cowling T.G. The Mathematical Theory of Non-Uniform Gases (1970), Cambridge University Press
4. Kogan M.N. Rarefied Gas Dynamics (1969), Plenum Press, New York
5. Markowich P.A., Ringhofer C.A., and Schmeiser C. Semiconductor Equations (1990), Springer, Wien
6. Dreyer W., and Struchtrup H. Heat pulse experiments revisited. Cont. Mech. Thermodyn. 5 (1993) 3-50
7. Chandrasekhar S. Radiative Transfer (1960), Dover Pub., London
8. Struchtrup H. Macroscopic transport equations for rarefied gas flows-approximation methods in kinetic theory. Interaction of Mechanics and Mathematics Series (2005), Springer, Heidelberg
9. Bobylev A.V. The Chapman-Enskog and Grad methods for solving the Boltzmann equation. Sov. Phys. Dokl. 27 (1982) 29-31
10. Rosenau P. Extending hydrodynamics via the regularization of the Chapman-Enskog solution. Phys. Rev. A 40 (1989) 7193-7196
11. Struchtrup H. Failures of the Burnett and Super-Burnett equations in steady state processes. Cont. Mech. Thermodyn. 17 (2005) 43-50
12. Grad H. On the kinetic theory of rarefied gases. Comm. Pure Appl. Math. 2 (1949) 331-407
13. Grad H. Principles of the kinetic theory of gases. In: Flügge S. (Ed). Handbuch der Physik XII: Thermodynamik der Gase (1958), Springer, Berlin
14. Müller I., and Ruggeri T. Rational Extended Thermodynamics. Springer Tracts in Natural Philosophy vol. 37 (1998), Springer, New York
15. Levermore C.D. Moment closure hierarchies for kinetic theories. J. Stat. Phys. 83 (1996) 1021-1065
16. Struchtrup H. Heat transfer in the transition regime: Solution of boundary value problems for Grad's moment equations via kinetic schemes. Phys. Rev. E 65 (2002) 041204
17. Struchtrup H. Grad's moment equations for microscale flows. 23rd Intl. Symposium on Rarefied Gas Dynamics. AIP Proceedings 663 (2003) 792-799
18. Struchtrup H., and Torrilhon M. Regularization of Grad's 13-moment-equations: Derivation and linear analysis. Phys. Fluids 15 (2003) 2668-2680
19. Torrilhon M., and Struchtrup H. Regularized 13-moment-equations: Shock structure calculations and comparison to Burnett models. J. Fluid Mech. 513 (2004) 171-198
20. Struchtrup H. Stable transport equations for rarefied gases at high orders in the Knudsen number. Phys. Fluids 16 (2004) 3921-3934
21. Struchtrup H., and Thatcher T. Bulk equations and Knudsen layers for the regularized 13 moment equations. Cont. Mech. Thermodyn. 19 (2007) 177-189
22. Gu X., and Emerson D. A computational strategy for the regularized 13 moment equations with enhanced wall-boundary conditions. J. Comp. Phys. 225 (2007) 263-283
23. Torrilhon M., and Struchtrup H. Boundary conditions for regularized 13-moment-equations for micro-channel-flows. J. Comp. Phys. 17 October (2007) 10.1016/j.jcp.2007.10.006 (published online)
24. Anile A.M., Romano V., and Russo G. Extended hydrodynamical model of carrier transport in semiconductors. SIAM J. Appl. Math. 61 (2000) 76-101
25. Struchtrup H. Extended moment method for electrons in semiconductors. Physica A 275 (2000) 229-255
26. Struchtrup H. On the number of moments in radiative transfer problems. Ann. Phys. 266 (1998) 1-26
27. Sone Y. Kinetic Theory and Fluid dynamics (2002), Birkhäuser, Boston
28. Maxwell J.C. On stresses in rarefied gases arising from inequalities of temperature. Phil. Trans. Roy. Soc. (London) 170 (1879) 231-256
29. Yuan G.-W. Convergence of PN approximation for the neutron transport equation with reflective boundary condition. J. Math. Phys. 41 (2000) 867-874
30. Sharipov F., and Seleznev V. Data on internal rarefied gas flows. J. Phys. Chem. Ref. Data 27 (1998) 657-706
31. Deutsch F. Best Approximations in Inner Product Spaces (2001), Springer, NewYork
32. Reitebuch D., and Weiss W. Application of high moment theory to the plane Couette flow. Contin. Mech. Thermodyn. 11 (1999) 217-225
33. Marques Jr. W., and Kremer G.M. Couette flow from a thirteen field theory with jump and slip boundary conditions. Contin. Mech. Thermodyn. 13 (2001) 207-217