On two-dimensional Riemann problem for pressure-gradient equations of the Euler system
type: Item
instance of: scholarly article
title: On two-dimensional Riemann problem for pressure-gradient equations of the Euler system
zbMATH Open document ID: 0956.35084
author: Peng Zhang
author: Jiequan Li
author: Tong Zhang
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: The authors consider the two-dimensional Riemann problem for the pressure-gradient equations with four pieces of initial data, which are restricted in such a way that only elementary waves appear at each interface. This model, which comes from the flux-splitting of the compressible Euler system, exhibits simpler patterns that in the complete Euler system. Therefore it makes it possible to clarify interactions of waves in two dimensions. In the present paper the authors analyze the structure of solutions and present numerical results to the two-dimensional Riemann problem. The results show that the slip lines have little influence on the structure of solutions, thus the interaction of rarefactions waves and shocks can be studied thoroughly. The authors give a criterion of transition from the regular reflection shock to the Mach reflection shock.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 65M99
Mathematics Subject Classification ID: 76N10
zbMATH DE Number: 1492546
zbMATH Keywords: interaction of rarefactions waves and shocks
zbMATH Keywords: slip line
zbMATH Keywords: regular reflection
zbMATH Keywords: Mach reflection
zbMATH Keywords: MmB scheme
MaRDI profile type: Publication
full work available at URL: dcds.1998.4.609
OpenAlex ID: W2027379249
DOI: 10.3934/DCDS.1998.4.609
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description: scientific article; zbMATH DE number 1492546