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: email@example.com
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.