Source: https://www.iejme.com/article/the-problem-of-interference-between-discontinuities-of-the-first-order
Timestamp: 2019-04-22 14:15:29+00:00

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Reference: Bulat PV. The problem of Interference between Discontinuities of the First Order. Int Elect J Math Ed. 2016;11(5), 1013-1021.
Reference: Bulat, P. V. (2016). The problem of Interference between Discontinuities of the First Order. International Electronic Journal of Mathematics Education, 11(5), 1013-1021.
Reference: Bulat, Pavel V.. "The problem of Interference between Discontinuities of the First Order". International Electronic Journal of Mathematics Education 2016 11 no. 5 (2016): 1013-1021.
Reference: Bulat, P. V. (2016). The problem of Interference between Discontinuities of the First Order. International Electronic Journal of Mathematics Education, 11(5), pp. 1013-1021.
Reference: Bulat, Pavel V. "The problem of Interference between Discontinuities of the First Order". International Electronic Journal of Mathematics Education, vol. 11, no. 5, 2016, pp. 1013-1021.
Reference: Bulat PV. The problem of Interference between Discontinuities of the First Order. Int Elect J Math Ed. 2016;11(5):1013-21.
The article discusses the problem of determining the differential characteristics of discontinuities, waves and currents behind them. In this paper research history of gas-dynamic discontinuities’ differential properties is discussed. The concept of weak discontinuities (discontinuous characteristics, discontinuities of first order) is analyzed. The differential conditions of dynamic compatibility, connecting curvatures of discontinuities with non-uniformities of the flow before and after them are given. The typical problems of interference between discontinuities of first order are provided: interaction of the shock with a weak tangential discontinuity and discontinuous characteristics, refraction of weak discontinuity on a tangential discontinuity, interference of weak discontinuities between themselves. The article presented typical interference problem of discontinuities of first order: interaction of the shock with a weak tangential discontinuity and discontinuity characteristics, refraction of weak discontinuity on a tangential discontinuity, interference of weak discontinuities between themselves. The practical importance of first order problems of interference of discontinuities is shown, because the discontinuity in first derivatives can lead to the formation of shock waves within the smooth flow - the so-called "suspended shock wave."
Adhemar, R. D. (1904) Sur une classe d’équations aux dérivées partielles de second ordre, du type hyperbolique. J. Math. Pures et Appl. Sér., 5(10), 131-207.
Adrianov, A. L. (2000) On model shock wave curvature in a pulsating flow. Computational Technologies, 5(6), 3-14.
Bulat, P. V. (2014) Reflection of a weak discontinuity of the axis and the plane of symmetry. American Journal of Applied Sciences, 11(6), 1025-1031.
Bulat, P. V., Bulat, M. P. (2015) Gas-dynamic Variable Relation on Opposite Sides of the Gas-dynamic Discontinuity. Research Journal of Applied Sciences, Engineering and Technology, 9(12), 1097-1104.
Bulat, P. V., Zasukhin, O. N. & Uskov, V. N. (1989) Development of an updated methodology for calculating the first barrel of a supersonic jet with the viscous effects. Leningrad Mechanical Institute report, 7432925.
Bulat, P. V., Zasukhin & O. N., Uskov, V. N. (1990) Calculation of the compressed layer of a supersonic jet. Proceedings of XV All-Union seminar on gas jets, 23 p.
Bulat, P. V., Zasukhin & O. N., Uskov, V. N. (1993) Formation of the jet during a smooth start of the Laval nozzle. Scientific notes of St. Petersburg State University. A series of mathematical sciences. “Gas dynamics and heat transfer,” 10, 1-22.
Bulat, P. V., Zasukhin, O. N. & Uskov, V. N. (2000). Investigation of the supersonic nozzle diffuser part influence on flow regimes and acoustic radiation of the jet. Proceedings of XVIII Intertational seminar “Gas and plasma flow in nozzles, jets and tracks”, 53p.
Bulat, P. V., Zasukhin, O. N., Uskov & V. N. (2002) Gas dynamics and acoustics of a supersonic jet, which expires in a channel with sudden expansion. In Modern Problems of Non-Equilibrium Gas Dynamics. St. Petersburg: BSTU press, 136-158.
Courant, R. & Friedrichs, K. O. (1948) Supersonic Flow and Shock Waves. New York: Springer. 322p.
Dyakov, S. P. (1957). Interaction of shock wave with small perturbations. Journal of Experimental and Theoretical Physics, 33(4), 948–973.
Katskova, O. N., Naumova, I. N., Shmyglevsky, Yu. D. & Shulinshina, N. P. (1961) Experience in Calculation of Plane and Axisymmetric Supersonic Gas Flows by Method of Characteristics. Moscow: Computing center of USSR Academy of Science. 363p.
Lighthill, M. J. (1949) Renormalized Coordinate Stretching: A Generalization of Shoot and Fit with Application to Stellar Structure. Phil. Mag, 40, 1179-1201.
Lighthill, M. J. (1957) Dynamics of a dissociating gas Part I Equilibrium flow. Journal of Fluid Mechanics, 2, 1-32.
Molder, S. (1979) Flow behind curved shock waves. University of Toronto Institute for Aerospace Studies Report, 217, 254-256.
Mostovykh, P. S. & Uskov, V. N., (2011) Compatibility conditions on a weak discontinuity in axisymmetric flows of non-viscous gas. Vestnik St. Petersburg University, 1(4), 123-133.
Omelchenko, A. V. (2002) Differential characteristic of the flow behind a shock wave. Technical Physics, 47(1), 18–25.
Pai, Shih-I. (1962). Introduction to the Theory of Compressible Flow. Moscow: Publishing House of Foreign Literatur, 344p.
Panov, D. Yu. (1957) The numerical solution of quasi-linear hyperbolic systems of differential equations in partial derivatives. Moscow, State publishing house of technical and theoretical literature. 224p.
Rusanov, V. V. (1973) Derivatives of the gasdynamic functions after curved shock wave. Keldysh Institute of Applied mathematics, 18p.
Silnikov, M. V., Chernyshov, M. V. & Uskov, V. N. (2014) Two-dimensional over-expanded jet flow parameters in supersonic nozzle lip vicinity. Acta Astronautica, 97, 38-41.
Truesdell, C. (1952) On curved shocks in steady plane flow of an ideal fluid. Journal of the Aeronautical Sciences, 19(12), 826-28.
Uskov, V. N. (1987) Analysis of the shock-wave structures in a non-uniform steady flow. Fundamental Problems of Physics of Shock Waves, 2, 166-69.
Uskov, V. N., Bulat, P. V. & Arkhipova, L. P. (2014) Gas-dynamic Discontinuity Conception. Research Journal of Applied Sciences, Engineering and Technology, 8(22), 2255-2259.
Uskov, V. N. & Mostovykh, P. S. (2012) Differential characteristics of shock waves and triple shock wave configurations. Proceedings of 20th International Shock Interaction Symposium, 211-214.
Whitham, G. B. (1974) Linear and Nonlinear Waves. New York: John Wiley&Sons. 654p.

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