BGK-Burnett equations for flows in the continuum-transition regime

Journal of thermophysics and heat transfer

Volumn 13, Issue 4, 1999, Pages 397-410

  Balakrishnan, Ramesh ^a   Agarwal, Ramesh K ^a   Yun, Keon Young ^a  

^a WICHITA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUUM MECHANICS; ENTROPY; FUNCTIONS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS;

BHATNAGAR-GROSS-KROOK (BGK)-BURNETT EQUATIONS; BOLTZMANN EQUATION; CHAPMAN-ENSKOG EXPANSION;

HYPERSONIC FLOW;

EID: 0033333798     PISSN: 08878722     EISSN: None     Source Type: Journal    
DOI: 10.2514/2.6464     Document Type: Article

References (15)

1. Bird, G. A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford Univ. Press, 1994.
2. Burnett, D., "The Distribution of Velocities and Mean Motion in a Slightly Non-Uniform Gas" Proceedings of the London Mathematics Society, Vol. 39, No. 2, 1935, pp. 382-435.
3. Chapman, S., and Cowling, T. G., The Mathematical Theory of Non-Uniform Gases, Cambridge Univ. Press, 1960.
4. Fiscko, K. A., and Chapman, D. R., "Comparison of Burnett, Super-Burnett and Monte-Carlo Solutions for Hypersonic Shock Structure," Vol. 118, Progress in Aeronautics and Astronautics, AIAA, Washington, DC, 1989, pp. 374-395.
5. Zhong, X., "Development and Computation of Continuum Higher-Order Constitutive Relations for High Altitude Hypersonic Flow," Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, Stanford Univ., CA, Aug. 1991.
6. Bobylev, A. V., "The Chapman-Enskog and Grad Methods for Solving the Boltzmann Equation," Soviet Physics - Doklady, Vol. 27, No. 1, 1982.
7. Welder, W. T., Chapman, D. R., and MacCormack, R. W., "Evaluation of Various Forms of the Burnett Equations," AIAA Paper 93-3094, July 1993.
8. Comeaux, K. A., Chapman, D. R., and MacCormack, R. W., "An Analysis of the Burnett Equations Based on the Second Law of Thermodynamics," AIAA Paper 95-0415, Jan. 1995.
9. Bhatnagar, P. L., Gross, E. P., and Krook, M., "Model for Collision Processes in Gases, I. Small Amplitude Processes in Charged and Neutral One-Component Systems," Physical Review, Vol. 94, No. 3, 1954, pp. 511-524.
10. Balakrishnan, R., and Agarwal, R. K., "A Kinetic Theory Based Scheme for the Numerical Solution of the BGK-Burnett Equations for Hypersonic Flows in the Continuum-Transition Regime," AIAA Paper 96-0602, Jan. 1996.
11. Balakrishnan, R., and Agarwal, R. K., "Entropy Consistent Formulation and Numerical Simulation of the BGK-Burnett Equations for Hypersonic Flows in the Continuum-Transition Regime," International Conf. for the Numerical Methods in Fluid Dynamics, Monterey, CA, June 1996.
12. Balakrishnan, R., and Agarwal, R. K., "Numerical Simulation of the BGK-Burnett for Hypersonic Flows," Journal of Thermophysics and Heat Transfer, Vol. 11, No. 3, 1997.
13. Deshpande, S. M., "On the Maxwellian Distribution, Symmetric Form and Entropy Conservation for the Euler Equations," NASA TP 2583, 1986.
14. Grad, H., "On the Kinetic Theory of Rarefied Gases," Communications on Pure and Applied Mechanics, Vol. 2, 1949, pp. 331-407.
15. Acheson, K. E., and Agarwal, R. K., "A Kinetic Theory Based Wave Particle Flux Splitting Scheme for Euler Equations," AIAA Paper 95-2178, 1995.