International Electronic Journal of Mathematics Education

The problem of Interference between Discontinuities of the First Order
  • Article Type: Research Article
  • International Electronic Journal of Mathematics Education, 2016 - Volume 11 Issue 5, pp. 1013-1021
  • Published Online: 29 Jul 2016
  • Article Views: 734 | Article Download: 577
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AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Bulat PV. The problem of Interference between Discontinuities of the First Order. Int Elect J Math Ed. 2016;11(5), 1013-1021.
APA 6th edition
In-text citation: (Bulat, 2016)
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.
Chicago
In-text citation: (Bulat, 2016)
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.
Harvard
In-text citation: (Bulat, 2016)
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.
MLA
In-text citation: (Bulat, 2016)
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.
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Bulat PV. The problem of Interference between Discontinuities of the First Order. Int Elect J Math Ed. 2016;11(5):1013-21.

Abstract

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."

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