On the \(2\)-D Riemann problem for the compressible Euler equations. II: Interaction of contact discontinuities
type: Item
instance of: scholarly article
title: On the \(2\)-D Riemann problem for the compressible Euler equations. II: Interaction of contact discontinuities
zbMATH Open document ID: 1032.76062
author: Tung Chang
author: Shuli Yang
author: Gui-Qiang Chen
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: The authors study the interaction of nonliner waves for the two-dimensional compressible Euler equations for gas dynamics: \[ \begin{cases} \rho_t+(\rho u)_x+(\rho v)_y=0\\ (\rho u)+(\rho u^2+p)_x+(\rho uv)_y=0\\ (\rho v)_t+(\rho uv)_x +(\rho v^2+p)=0\\ \left(\rho\left (e+{u^2+v^2\over 2}\right) \right)_t+ \left(\rho u\left(h +{u^2+v^2\over 2}\right)\right)_x+\left(\rho v\left(h+ {u^2 +v^2 \over 2}\right) \right)_y=0,\end{cases} \] where \(\rho,p\), and \((u,v)\) represent the density, the pressure, and the velocity, respectively; the internal energy \(e\) and the enthalpy \(h\) are determined by \(e={p\over(\gamma-1) \rho}\) with \(1<\gamma\leq 3\) and \(h=e+ {P\over\rho}\), respectively. In this paper, the authors focus mainly on the interation of contact discontinuities, which consists of two different cases. For each case the authors analyze the structure of Riemann solution. For Part I, cf. ibid. 1, 555-584 (1995; Zbl 0874.76031).
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 1492641
zbMATH Keywords: compressible Euler equation
zbMATH Keywords: gas dynamics
zbMATH Keywords: contact discontinuities
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: dcds.2000.6.419
OpenAlex ID: W2066741072
DOI: 10.3934/DCDS.2000.6.419
Recommended article: On the 2-D Riemann problem for the compressible Euler equations I: Interaction of shocks and rarefaction waves
Recommended article: Two-dimensional Riemann problems for the compressible Euler system
Recommended article: On the Riemann problem for 2D compressible Euler equations in three pieces
Recommended article: Two-dimensional Riemann problems: from scalar conservation laws to compressible Euler equations
Recommended article: Q5493665
Recommended article: Classification of the Riemann problem for compressible two-dimensional Euler system in non-ideal gas
Recommended article: The Riemann problem for the two-dimensional zero-pressure Euler equations
Recommended article: Q5455474
Recommended article: Compressible Euler equations with second sound: asymptotics of discontinuous solutions
Recommended article: On two-dimensional Riemann problem for pressure-gradient equations of the Euler system
description: scientific article; zbMATH DE number 1492641