This article discusses the history of study of shock-wave structures arising at a clash of the shock wave on a wedge. We introduce the concept of regular and Mach reflection. We consider von Neumann three-wave model containing a branching shock wave, main and reflected discontinuities, a tangential discontinuity (sliding surface) behind the shock waves line of intersection. Experiments on studying Mach reflection at low Mach numbers and small angle of the wedge are described. The main works devoted to J. Neumann paradox when at low Mach number Mach reflection, in accordance with the theory, cannot exist, but, nevertheless, is observed in the experiments. The work is useful for engineers and scientists to compile a basic overview of the problem of Mach reflection.

• Ben-Dor, G. & Glass, I. I. (1980) Domains and boundaries of non-stationary oblique shock-wave reflexions. 2. Monatomic gas. Journal of Fluid Mechanics, 96(4), 735-756.
• Bleakney, W., Fletcher, C. H. & Weimer, D. K. (1949) The density field in mach reflection of shock waves. Physical Review, 76, 323-324.
• Bleakney, W. & Taub, A. H. (1949) Interaction of shock waves. Review of Modern Physics, 21, 584.
• Breed, B. R. (1967) Impossibility of three confluent shocks in two-dimensional irrotational flow. Physics of Fluids, 10(1), 21-23.
• Brown, G. L. & Roshko, A. (1974) On density effects and large structure in turbulent mixing layers. Journal of Fluid Mechanics, 64(4), 775-816.
• Courant, R. & Friedrichs, K. O. (1948) Supersonic flow and shock waves. New York: Interscience, 464 p
• Dash, S. M. & Roger, D. T. (1981) Shock-Capturing model for one- and two-phase supersonic exhaust flow. AIAA Journal, 19(7), 842-851.
• Dulov, V. G. (1973) Motion of triple configuration of shock waves with formation of wake behind branching point. Journal of Applied Mechanics and Technical Physics, 14(6), 791-797.
• Kawamura, R. & Saito, H. (1956) Reflection of Shock Waves-1 Pseudo-Stationary Case. Journal of the Physical Society of Japan, 11(5), 584-592.
• Landau, L. D. & Lifshitz, E. M. (2003) Theoretical Physics. London: Publishing house “Fizmatlit”. 257p.
• Law, C. K. (1970) Diffraction of strong shock waves by a sharp compressive corner. Toronto: University of Toronto Institute for Aerospace. 150p.
• Lee, J. H. & Glass, I. I. (1984) Pseudo-stationary oblique-shock-wave reflections in frozen and equilibrium air. Progress in Aerospace Sciences, 21, 33-80.
• Mach, E. Uber den Verlauf von Funkenwellen in der Ebene und im Raume. Sitzungsbr Akad Wien, 78, 819-838.
• Melnikov, D. A. (1962) Reflection of shock waves from the axis of symmetry. Journal of USSR Academy of Science. Mechanics and Mechanical Engineering, 3, 24-30.
• Neumann, J. (1943) Oblique reflection of shocks. In A.H. Taub (ed.) John von Neumann Collected Works, 4, 238-299.
• Ragab, S. A. & Wu, J. L. (1989) Linear instabilities in two-dimensional compressible mixing layers. Physics of Fluids A: Fluid Dynamics, 1(6), 957-966.
• Sakurai, A. (1964) On the problem of weak mach reflection. Journal of the Physical of Japan, 19(8), 1440-1450.
• Smith, L. G. (1945) Photographic investigations of the reflection of plane shocks in air. Office of Scientific Research and Development, Report, 6271.
• Sternberg, J. (1959) Triple-Shock-Wave Intersections. Physics of Fluids, 2(2), 179-206.
• Uskov, V. N., Bulat, P. V. & Prodan, N. V. (2012) Rationale for the use of models of stationary mach configuration calculation of mach disk in a supersonic jet. Fundamental Research, 11(1), 168-175.
• Uskov, V. N., Chernyshov, M. V. (2009) Triple configurations of stationary shock waves. Proceedings of XII All-Russian Scientific-Practical Conference, 420-435.
• Uskov, V. N. & Mostovykh, P. S. (2008) Triple configurations of traveling shock waves in inviscid gas flows. Journal of Applied Mechanics and Technical Physics, 49(3), 347-353.
• Uskov, V. N. & Mostovykh, P. S. (2011) Triple-Shock-Wave Configurations: Comparison of Different Thermodynamic Models for Diatomic Gases. Proceedings of 28th International Symposium on Shock Waves, 1-7.
• Vasilev, E. I. (1999) Four-wave scheme of weak Mach shock waves interaction under the von Neumann paradox conditions. Fluid Dynamics, 34(3), 421-27.
• Vasilev, E. I. & Kraiko, A. N. (1999) Numerical simulation of weak shock diffraction over a wedge under the von Neumann paradox conditions. Journal of Computational Mathematics and Mathematical Physics, 39(8), 1393-1404. 

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