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 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
