Math. Model. Nat. Phenom.
Volume 13, Number 2, 2018
Shock Waves, Discontinuities and Singularities in Natural Phenomena
|Number of page(s)||13|
|Published online||20 June 2018|
Generalized Riemann waves and their adjoinment through a shock wave
School of Mathematics, Institute of Science, Suranaree University of Technology,
★ Corresponding author: firstname.lastname@example.org
Accepted: 16 October 2017
Generalized simple waves of the gas dynamics equations in Lagrangian and Eulerian descriptions are studied in the paper. As in the collision of a shock wave and a rarefaction wave, a flow becomes nonisentropic. Generalized simple waves are applied to describe such flows. The first part of the paper deals with constructing a solution describing their adjoinment through a shock wave in Eulerian coordinates. Even though the Eulerian form of the gas dynamics equations is most frequently used in applications, there are advantages for some problems concerning the gas dynamics equations in Lagrangian coordinates, for example, of being able to be reduced to an Euler–Lagrange equation. Through the technique of differential constraints, necessary and sufficient conditions for the existence of generalized simple waves in the Lagrangian description are provided in the second part of the paper.
Mathematics Subject Classification: 35Q31 / 76M60 / 76N15
Key words: The gas dynamics equations / Riemann waves / shock wave
© EDP Sciences, 2018
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