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On simulation methods for the Boltzmann equation. (English) Zbl 0623.76084

We give a comparative discussion of some simulation procedures for the Boltzmann equation in terms of rigour and numerical effort. The methods under consideration are the algorithms suggested by G. A. Bird [Molecular gas dynamics, Clarendon Press (1976)] and K. Nanbu [J. Phys. Soc. Japan 49, 2042-2049 (1980)], respectively, and a modification of the Nanbu procedure suggested by H. Babovsky [Math. Methods Appl. Sci. 8, 223-233 (1986; Zbl 0609.76084)]. The procedures are applied to and compared by means of a shock wave problem.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics

Citations:

Zbl 0609.76084
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References:

[1] Alsmeyer H., J. Fluid Mech. 74 pp 497– (1976) · doi:10.1017/S0022112076001912
[2] Babovsky H., Math. Meth. Appl. Sci. 9 (1986)
[3] Belotserkovskiy O. M., Yanitzkiy, V.Ye.: Zhurn. Vych. Mat. i. Mat. Fiz. 15 pp 1195– (1975)
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[5] Bird G. A., AIAA Journal 4 pp 55– (1966) · doi:10.2514/3.3384
[6] Bird G. A., Phys. Fluids 13 pp 2676– (1970) · Zbl 0227.76111 · doi:10.1063/1.1692849
[7] Bird G. A., Molecular Gas Dynamics, Clarendon Press (1976)
[8] Deshpande S. M., Report 18 FM 4, Dept. Aero Engng., Indian Inst. Science (1978)
[9] Nanbu K., J. Phys. Soc. Jpn. 49 pp 2042– (1980) · doi:10.1143/JPSJ.49.2042
[10] Nanbu K., J. Phys. Soc. Jpn. 50 pp 3382– (1983) · doi:10.1143/JPSJ.52.3382
[11] Nanbu K., Phys. Fluids 27 pp 2632– (1984) · doi:10.1063/1.864565
[12] Papanicolaou G. C., Bull. Am. Math. Soc. 81 pp 330– (1975) · Zbl 0361.60056 · doi:10.1090/S0002-9904-1975-13744-X
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