Nonisentropic Solutions of Simple Wave Type of the Gas Dynamics Equations

DOI

10.1142/S1402925111001374How to use a DOI?

Keywords

Differential constraints; compatibility conditions; Riemann (simple) waves; gas dynamics equations

Abstract

The manuscript is devoted to nonisentropic solutions of simple wave type of the gas dynamics equations. For an isentropic flow these equations (in one-dimensional and steady two-dimensional cases) are reduced to the equations written in the Riemann invariants. The system written in the Riemann invariants is hyperbolic and homogeneous. It allows obtaining simple waves, which are also called Riemann waves. For nonisentropic flows there are no Riemann invariants. The question is: what solutions could substitute the Riemann waves? By the method of differential constraints such types of solutions are found here. For these classes of solutions one can integrate the gas dynamics equations: finite formulas with one parameter are obtained. These solutions have some properties similar to simple Riemann waves. For example, they describe a nonisentropic rarefaction wave. The rarefaction waves play the main role in many applications such as the problem of pulling a piston, decay of arbitrary discontinuity and others.

Copyright

© 2011 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Sergey V. Meleshko
AU  - Vasilii P. Shapeev
PY  - 2021
DA  - 2021/01/07
TI  - Nonisentropic Solutions of Simple Wave Type of the Gas Dynamics Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 195
EP  - 212
VL  - 18
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001374
DO  - 10.1142/S1402925111001374
ID  - Meleshko2021
ER  -