Boundary conditions for regularized 13-moment-equations for micro-channel-flows

Journal of Computational Physics

Volumn 227, Issue 3, 2008, Pages 1982-2011

  Torrilhon, Manuel ^a   Struchtrup, Henning ^a,b  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Boundary value problem; Continuum models; Kinetic gas theory; Micro channels; R13 equations

Indexed keywords

BOLTZMANN EQUATION; BOUNDARY CONDITIONS; CONTINUUM MECHANICS; KINETICS; MAXWELL EQUATIONS; NUMERICAL METHODS; SHEAR FLOW;

BOLTZMANN'S EQUATIONS; BOUNDARY-VALUE PROBLEM; CONTINUUM MODEL; KINETIC GAS THEORY; MICRO CHANNELS; MICRO-FLOW; MICROCHANNEL FLOW; R13 EQUATION; RAREFIED FLOW; REGULARIZED 13 MOMENT EQUATIONS;

BOUNDARY VALUE PROBLEMS;

EID: 37249021809     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.10.006     Document Type: Article

References (39)

1. Ansumali S., Karlin I.V., Arcidiacono S., Abbas A., and Prasianakis N.I. Hydrodynamics beyond Navier-Stokes: exact solutions to the lattice Boltzmann hierarchy. Phys. Rev. Lett. 98 (2007) 124502
2. Agarwal R.K., Yun K.Y., and Balakrishnan R. Beyond Navier-Stokes: Burnett equations for flows in the continuum-transition regime. Phys. Fluids 13 (2001) 3061-3085 Erratum: Phys. Fluids 14 (2002) 1818
3. Au J.D., Torrilhon M., and Weiss W. The shock tube study in extended thermodynamics. Phys. Fluids 13 8 (2001) 2423-2432
4. Bird G.A. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. second ed. (1998), Oxford University Press, New York
5. Bobylev A.V. The Chapman-Enskog and Grad methods for solving the Boltzmann equation. Sov. Phys. Dokl. 27 (1982) 29-31
6. Bobylev A.V. Instabilities in the Chapman-Enskog expansion and hyperbolic Burnett equations. J. Stat. Phys. 124 2-4 (2006) 371-399
7. Cercignani C. The Boltzmann Equation and its Applications. Applied Mathematical Sciences vol. 67 (1988), Springer, New York
8. Chapman S., and Cowling T.G. The Mathematical Theory of Non-Uniform Gases (1970), Cambridge University Press, Cambridge
9. Eu B.-C. A modified moment method and irreversible thermodynamics. J. Chem. Phys. 73 6 (1980) 2958-2969
10. Grad H. On the Kinetic Theory of Rarefied Gases. Commun. Pure Appl. Math. 2 (1949) 331-407
11. Grad H. Principles of the Kinetic Theory of Gases. In: Flügge S. (Ed). Handbuch der Physik vol. 12 (1958), Springer, Berlin
12. Gu X., and Emerson D. A computational strategy for the regularized 13 moment equations with enhanced wall-boundary conditions. J. Comput. Phys. 225 (2007) 263-283
13. Jin S., and Slemrod M. Regularization of the Burnett equations via relaxation. J. Stat. Phys. 103 5-6 (2001) 1009-1033
14. Karniadakis G.E., and Beskok A. Micro Flows: Fundamentals and Simulation (2001), Springer, New York
15. Knudsen M. Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren. Ann. Phys. 333 (1909) 75-130
16. Levermore C.D. Moment closure hierarchies for kinetic theories. J. Stat. Phys. 83 5-6 (1996) 1021-1065
17. Lockerby D.A., and Reese J.M. High-resolution Burnett simulations of micro Couette flow and heat transfer. J. Comput. Phys. 188 2 (2003) 333-347
18. Maxwell J.C. On stresses in rarefied gases arising from inequalities of temperature. Phil. Trans. Roy. Soc. (London) 170 (1879) 231-256
19. Müller I., and Ruggeri T. Rational Extended Thermodynamics. Springer Tracts in Natural Philosophy. second ed. vol. 37 (1998), Springer, New York
20. Müller I., Reitebuch D., and Weiss W. Extended thermodynamics - consistent in order of magnitude. Cont. Mech. Thermodyn. 15 2 (2003) 411-425
21. Myong R.-S. A computational method for Eu's generalized hydrodynamic equations of rarefied and microscale gas dynamics. J. Comput. Phys. 168 1 (2001) 47-72
22. Ohwada T., Sone Y., and 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 12 (1989) 2042-2049
23. Rosenau P. Extending hydrodynamics via the regularization of the Chapman-Enskog expansion. Phys. Rev. A 40 (1989) 7193-7196
24. Seeger S., and Hoffmann H. The Comulant method in computational kinetic theory. Cont. Mech. Therm. 12/6 (2000) 403
25. Sharipov F., and Seleznev V. Data on internal rarefied gas flows. J. Phys. Chem. Ref. Data 27 3 (1998) 657-706
26. Struchtrup H. Macroscopic Transport Equations for Rarefied Gas Flows. Interaction of Mechanics and Mathematics (2005), Springer, New York
27. H. Struchtrup, Grad's moment equations for microscale flows, in: 23rd International Symposium on Rarefied Gas Dynamics, AIP Proceedings, vol. 663, 2003, pp. 792-799.
28. Struchtrup H. Stable transport equations for rarefied gases at high orders in the Knudsen number. Phys. Fluids 16 11 (2004) 3921-3934
29. Struchtup H., and Thatcher T. Bulk equations and Knudsen layers for the regularized 13 moment equations. Cont. Mech. Thermodyn. 19 3 (2007) 177-189
30. Struchtrup H., and Torrilhon M. Regularization of Grad's 13-moment-equations: derivation and linear analysis. Phys. Fluids 15/9 (2003) 2668-2680
31. Struchtrup H., and Torrilhon M. H-theorem, regularization, and boundary conditions for linearized 13 moment equations. Phys. Rev. Lett. 99 (2007) 014502
32. Y. Suzuki, B. van Leer, Application of the 10-moment model to MEMS flows, 43rd AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2005-1398, 2005.
33. T. Thatcher, Microscale Gas Flow: A Comparison of Grad's 13 Moment Equations and Other Continuum Approaches, Masters Thesis, Dept. Mech. Eng., Univ. of Victoria, Canada, 2005.
34. Torrilhon M. Two-dimensional bulk microflow simulations based on regularized 13-moment-equations. SIAM Multiscale Model. Simul. 5 3 (2006) 695-728
35. M. Torrilhon, Regularized 13-moment-equations, in: 25th International Symposium on Rarefied Gas Dynamics, St. Petersburg, Russia, 2006.
36. Torrilhon M., and Struchtrup H. Regularized 13-moment-equations: shock structure calculations and comparison to Burnett models. J. Fluid Mech. 513 (2004) 171-198
37. Vincenti W.G., and Kruger Jr. C.H. Introduction to Physical Gas Dynamics (1965), Wiley, New York
38. Xu K., and Li Z.-H. Microchannel flow in the slip regime: gas-kinetic BGK-Burnett solutions. J. Fluid Mech. 513 (2004) 87-110
39. Zheng Y., Garcia A.L., and Alder J.B. Comparison of kinetic theory and hydrodynamics for Poiseuille flow. J. Stat. Phys. 109 (2002) 495-505