International Electronic Journal of Mathematics Education

Gas-dynamic Waves and Discontinuities
  • Article Type: Research Article
  • International Electronic Journal of Mathematics Education, 2016 - Volume 11 Issue 5, pp. 1101-1111
  • Published Online: 02 Aug 2016
  • Article Views: 720 | Article Download: 748
  • Open Access Full Text (PDF)
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Bulat PV, Uskov VN. Gas-dynamic Waves and Discontinuities. Int Elect J Math Ed. 2016;11(5), 1101-1111.
APA 6th edition
In-text citation: (Bulat & Uskov, 2016)
Reference: Bulat, P. V., & Uskov, V. N. (2016). Gas-dynamic Waves and Discontinuities. International Electronic Journal of Mathematics Education, 11(5), 1101-1111.
Chicago
In-text citation: (Bulat and Uskov, 2016)
Reference: Bulat, Pavel V., and Vladimir N. Uskov. "Gas-dynamic Waves and Discontinuities". International Electronic Journal of Mathematics Education 2016 11 no. 5 (2016): 1101-1111.
Harvard
In-text citation: (Bulat and Uskov, 2016)
Reference: Bulat, P. V., and Uskov, V. N. (2016). Gas-dynamic Waves and Discontinuities. International Electronic Journal of Mathematics Education, 11(5), pp. 1101-1111.
MLA
In-text citation: (Bulat and Uskov, 2016)
Reference: Bulat, Pavel V. et al. "Gas-dynamic Waves and Discontinuities". International Electronic Journal of Mathematics Education, vol. 11, no. 5, 2016, pp. 1101-1111.
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Bulat PV, Uskov VN. Gas-dynamic Waves and Discontinuities. Int Elect J Math Ed. 2016;11(5):1101-1.

Abstract

In this paper we examine the history of the studying the dynamic compatibility conditions for gas-dynamic discontinuities, which determine the ratio between values of the gas-dynamic variables before the discontinuity and right behind him. The concepts of a shock wave, shock and the shock polar are introduced. The formation of ideas about the shock waves as a narrow region with abrupt changes in gas-dynamic parameters is shown with a staged scientific studies as an example. The relationship between the physical nature of gas-dynamic discontinuities and the appearance of singularities in solutions of the Euler equations for an ideal gas is shown. Burgers equation, which allows to simulate the shock waves is discussed. The article can serve as a brief introduction to the theory of gasdynamic discontinuities. It proposes the modern idea of gasdynamic discontinuities as the features arising in the solution of hyperbolic partial differential equations.

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