Abstract
The direct simulation Monte Carlo (DSMC) method is applied to simulation of nonstationary Mach reflection of strong shock waves. Normally the DSMC method is very time consuming in solving unsteady flow field problems especially for high Mach numbers, because of the necessity of iterative calculations to eliminate the inherent statistical fluctuation caused by a finite sample size. A central weighted smoothing technique is introduced to process the DSMC results, so that the iteration time can be significantly reduced. In spite of some relaxations of the shock wave structure, the smoothing technique is verified to be useful to estima te the flow fields qualitatively and even quantitatively by using a relatively small sample size. The comparison between the present approach and the kineticmodel approach (Xu et al. 1991a, 1991b) on the application to unsteady rarefied flow fields was also carried out.
Similar content being viewed by others
References
Auld DJ, Bird GA (1977) Monte-Carlo simulation of regular and Mach reflection. AIAA J 15:638–641
Bird GA (1976) Molecular gas dynamics. Oxford, Clarendon
Guest PG (1961) Numerical methods of curve fitting. Univ Press, Cambridge, England
Mach E (1878) Akademie der Wissenchaften. Wien 77:1228
von Neumann J (1963) Collected works, 6, Pergamon
Schmidt B (1989) Structure of incipient triple point at the transition from regular reflection to Mach reflection. In: Muntz EP et al. (eds) Rarefied gas dynamics: Theoretical and computational techniques. AIAA Inc Washington DC, pp 597
Schmidt B, Fuchs J (1991) Results about the structure of the shock wave reflection process for strong incoming shock waves. In: Honma H (ed) Proc Int Workshop on Strong Shock Waves, pp 125
Seiler F (1985) Pseudo-stationary Mach reflection of shock waves. In: Bershader D, Hanson RK (eds) Shock Waves and Shock Tube. Proc 15th Int Symp on Shock Tubes. Stanford Univ Press, Stanford, California, pp 129
Walenta ZA (1980) Microscopic structure of the Mach-type reflection of the shock wave. Arch Mech, Warszawa 32:819–852
Walenta ZA (1983) Formulation of the Mach type reflection of shock waves. Arch Mech, Warszawa 35:187–196
Walenta ZA (1987) Mach reflection of a moving, plane shock wave under rarefied flow conditions. In: Grönig H (ed) Shock Waves and Shock Tubes. Proc 16th Int Symp on Shock Waves and Tubes. VCH Verlagsgesellschaft, Weinheim, pp 535
Xu DQ, Honma H (1991a) Numerical simulation for nonstationary Mach reflection of a shock wave: A kinetic-model approach. Shock Waves 1:43–49
Xu DQ, Honma H, Abe T (1991b) A numerical method for a kinetic equation and its application to propagating shock waves. Computers and Fluids 19, 3–4:297–304
Author information
Authors and Affiliations
Additional information
This article was processed using Springer-Verlag TEX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.
Rights and permissions
About this article
Cite this article
Xu, D.Q., Honma, H. & Abe, T. DSMC approach to nonstationary Mach reflection of strong incoming shock waves using a smoothing technique. Shock Waves 3, 67–72 (1993). https://doi.org/10.1007/BF01414749
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01414749