Comparison of Solution Methods for some Classical Flow Problems in Rarified Gas Dynamics

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References

[1] E. B. Hauser, “Analytical Solution for Three-Dimensional Discrete Ordinates Problems,” Proceedings of 12th Pan-American Congress of Applied Mechanic, Trinidad, 2-6 January 2012, pp. 1-5.
http://www.aamech.org/PACAM12/Documents/73.pdf

[2] C. S. Scherer, J. F. Prolo Fihlo and L. B. Barichello, “An Analytical Approach to the Unified Solution of Kinetic Equations in Rarefied Gas Dynamics. I. Flow Problems”. Zeitschrift für Angewandte Mathematik und Physik ZAMP, Vol. 60, No. 1, 2009, pp. 70-115.

[3] C. S. Scherer, J. F. Prolo Filho and L. B. Barichello, “An Analytical Approach to the Unified Solution of Kinetic Equations in the Rarefied Gas Dynamics. II. Heat Transfer Problems” Zeitschrift für Angewandte Mathematik und Physik ZAMP, Vol. 60, No. 4, 2009, pp. 651-687.

[4] S. Taguchi and K. Aoki, “Numerical Analysis of Rarefied Gas Flow induced around a Flat Plate with a Single Heated Side in Rarefied Gas Dynamics,” Proceedings of 27th International Symposium on Rarefied Gas Dynamics, Pacific Grove, 10-15 July 2010, pp. 790-795.

[5] V. A. Titarev, “Efficient Deterministic Modeling of Three-Dimensional Rarefied Gas Flow,” Communications in Computational Physics, Vol. 12, No. 1, 2012, pp. 162-192.

[6] J. Y. Yang, B. P. Muljadi, Z. H. Li and H. X. Zhang, “A Direct Solver for Initial Value Problems of Rarefied Gas Flows of Arbitrary Statistics,” Communications in Computational Physics, Vol. 14, No. 1, 2013, pp. 242-264.

[7] C. Cercignani, “Mathematical Methods in Kinetic Theory,” Plenum Press, New York, 1969.

[8] C. Cercignani “Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations,” Cambridge University Press, Cambridge, 2000.

[9] C. Cercignani and A. Daneri, “Flow of Rarefied Gas between two Parallel Plates,” Journal of Applied Physics, Vol. 34 No. 12, 1962. pp. 3509-3513
doi:10.1063/1.1729249

[10] C. E. Siewert and L. B. Barichello, “A Discrete-Ordinate Solution for Poiseuille Flow in Plan Channel,” Zeitschrift für Angewandte Mathematik und Physik ZAMP, Vol. 50, No. 6, 1999, pp. 972-981. doi:10.1007/s000000050189

[11] S. K. Stefanov, V. M. Roussinov and C. Cerciginani, “Three-Dimensional Rayleigh-Benard Convection of a Rarefied Gas: DSMC and Navier-Stokes Calculations,” AIP Conference Proceedings of 24th International Symposium on Rarefied Gas Dynamics, Vol. 762, 2004, pp. 529-534.

[12] Y. Sone, “Rarefied Gas Flow Induced between Non-Parallel Plane Walls with Different Temperature,” In: M. Becker and M. Fiebig, Eds., Rarefied Gas Dynamics, DFVLR Press, Porz-Wahn, 1974.

[13] L. B. Barichello, M. Camargo, P. Rodrigues and C. E. Siewert, “Unified Solutions to Classical Flow Problems Based on the BGK Model,” Zeitschrift für Angewandte Mathematik und Physik ZAMP, Vol. 52, No. 3, 2001, pp. 517-534.

[14] C. S. Scherer and L. B. Barichello, “An Analytical Approach to the Unified Solution of Kinetic Equations in Rarefied Gas Dynamics. III. Evaporation and Condensation Problems,” Zeitschrift für Angewandte Mathematik und Physik ZAMP, Vol. 61, No. 1, 2012, pp. 95-117.

[15] S. Kosuge, K. Aoki and S. Takata, “Heat Transfer in a Gas Mixture between Two Parallel Plates: Finite-Difference Analysis of the Boltzmann Equation,” 22nd International Symposium on Rarefied Gas Dynamics, Sydney, 9-14 July 2000, pp. 289-296.

[16] B. P. Muljadi and J. Y. Yang, “Deterministic Solver for Rarefied Flow Problems of Gases of Arbitrary Statistics Based on the Semiclassical Boltzmann-BGK Equation,” 7th International Conference on Computational Fluid Dynamics, Big Island, 9-13 July 2012, p. 1404.

[17] R. D. M. Garcia and C. E. Siewert, “Particular Solutions of the Linearized Boltzmann Equation for A Binary Mixture of Rigid Spheres,” Zeitschrift für Angewandte Mathematik und Physik ZAMP, Vol. 59, No. 2, 2008, pp. 281-292.

[18] C. Henri, “Couette Flow for a Gas with a Discrete Velocity Distribution” Journal of Fluid Mechanics, Vol. 76, No. 2, 1976, pp. 273-287. doi:10.1017/S0022112076000633

[19] S. L. Lorenzani, A. Gibelli, A. Frezzotti, A. Frangi and C. Cercignani, “Kinetic Approach to Gas Flows in Microchannels,” Nanoscale and Microscale Thermophysical Engineering, Vol. 11, No. 1-2, 2007, pp. 211-226.
doi:10.1080/15567260701333489

[20] S. K. Loyalka, “Motion of a Sphere in a Gas: Numerical Solution of the Linearized Boltzmann Equation,” Physics of Fluids A: Fluid Dynamics, Vol. 4, No. 5, 1992, p. 1049.
doi:10.1063/1.858256

[21] S. Kubota and Y. Yoshizawa, “Couette Flow Problems by Thirteen Moment Equations,” Proceedings of Rarefied Gas Dynamics, DFVLR Press, Porz-Wahn, 1974.

[22] C. E. Siewert, “A Discrete-Ordinate Solution for Heat Transfer in a Plan Channel,” Journal of Computational Physics, Vol. 152, No. 1, 1999, pp. 251-263.
doi:10.1006/jcph.1999.6244

[23] M. M. R. Williams, “A Review of the Rarefied Gas Dynamics Theory Associated with Some Classical Problems in Flow and Heat Transfer,” Zeitschrift für Angewandte Mathematik und Physik ZAMP, Vol. 52, No. 3, 2001, pp. 500-516.

[24] P. L. Bhatnagar, E. P. Gross and M. Krook, “A Modelfor Collision Processes in Gases. 1. Small Amplitude Processes in Charge and Neutral One-Component Systems,” Physical Review, Vol. 94, No. 3, 1954, pp. 511-525.

[25] S. Takata, Y. Sone and K. Aoki, “ Numerical Analysis of a Uniform Flow of a Rarefied Gas Past a Sphere on the Basis of the Boltzmann Equation for Hard-Sphere Molecules,” Physics of Fluids A: Fluid Dynamics, Vol. 5, No. 3, 1993, p. 716. doi:10.1063/1.858655

[26] S. K. Lokalka and K. A. Hickey, “Kinetic Theory of Thermal Transpiration and Mechanocaloric Effect: Planar Flow of a Rigid Sphere Gas with Arbitrary Accommodation at the Surface,” Journal of Vacuum Science & Technology A, Vol. 9, No. 1, 1991, p. 158.
doi:10.1116/1.577119

[27] D. Valougeorgis, “An Analytic Solution of S-Model Kinetic Equations,” Zeitschrift für Angewandte Mathematik und Physik ZAMP, Vol. 54, No. 1, 2003, pp. 112-124.
doi:10.1007/PL00012627