A numerical method for a kinetic equation and its application to propagating shock waves. (English) Zbl 0732.76060
Summary: An efficient numerical method for kinetic equations and its application to analyses of moving shock wave problems are presented. The present study aims to give an efficient scheme for two-dimensional unsteady gas flows. An explicit MacCormack difference method is applied to solve a BGK-model equation. The efficiency and accuracy of the scheme are examined in an application to one-dimensional shock structure problems. Furthermore, the scheme is applied to a two-dimensional flow problem: nonstationary reflection of a shock wave at a wedge. The present scheme is found to be useful and efficient for the analyses of two-dimensional unsteady rarefied gas flows.
MSC:
76M20 | Finite difference methods applied to problems in fluid mechanics |
76L05 | Shock waves and blast waves in fluid mechanics |
76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
Keywords:
kinetic equations; moving shock wave; MacCormack difference method; BGK- model equation; two-dimensional unsteady rarefied gas flowsReferences:
[1] | Oguchi, H.; Morinishi, K.; Satofuka, N., Time-dependent approach to kinetic analyses of two-dimensional rarefied gas flows, (Beloserkovskii, O. M.; Kogan, M. N.; Kutateladze, C. S.; Rebrov, A. K., Rarefied Gas Dynamics (1985)), 293 |
[2] | (Doctoral Thesis of K. Morinishi (1985), Univ. Tokyo) |
[3] | MacCormack, R. W.; Warming, R. F., A numerical method for solving the equation of compressible viscous flow, AIAA Paper 81-110R (1981) |
[4] | Auld, D. J.; Bird, G. A., The transition from regular to Mach reflection, (Presented at the 9th Fluid and Plasma Dynamics Conf.. Presented at the 9th Fluid and Plasma Dynamics Conf., San Diego, Calif. (1976)) |
[5] | Seiler, F., Pseudo-stationary Mach reflection of shock waves, (Bershader, D.; Hanson, R., Shock Waves and Shock Tube (1985)), 129 |
[6] | Walenta, Z. A., Microscopic structure of the Mach-type reflection of the shock wave, Archwm. Mech. Stosow., 32, 819 (1980) |
[7] | Henderson, L. F.; Gray, P. M., Experiments on the diffraction of strong blast waves, (Proc. R. Soc. Lond., A377 (1981)), 363 |
[8] | Walenta, Z. A., Mach reflection of a moving, plane shock wave under rarefied flow conditions, (Grönig, H., Shock Waves and Shock Tubes (1987)), 545 |
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