A unified coordinate system for solving the two-dimensional Euler equations
type: Item
instance of: scholarly article
title: A unified coordinate system for solving the two-dimensional Euler equations
zbMATH Open document ID: 0969.76061
author: Yanyan Li
published in: Journal of Computational Physics
publication date: 2000-01-05T00:00:00Z
review text: For two-dimensional gas dynamical Euler equations, the authors introduce a unified coordinate system in which the flow variables are functions of time and of some permanent identification of pseudo-particles which move with velocity \(hq\), \(q\) being the velocity of fluid particles. This coordinate system includes Eulerian coordinates as a special case when \(h=0\), and Lagrangian ones when \(h=1\). The two-dimensional unsteady Euler equations in the unified coordinates are found to be hyperbolic for all values of \(h\), except when \(h=1\) (i.e. in Lagrangian coordinates). In the latter case Euler equations are only weakly hyperbolic, lacking one eigenvector, although all eigenvalues are real. The authors discuss the consequences of this deficiency of Lagrangian coordinates in connection with numerical computations.
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 76N15
zbMATH DE Number: 1384964
zbMATH Keywords: inviscid compressible flow
zbMATH Keywords: slip lines
zbMATH Keywords: hyperbolicity
zbMATH Keywords: weak hyperbolicity
zbMATH Keywords: two-dimensional gas dynamical Euler equations
zbMATH Keywords: unified coordinate system
zbMATH Keywords: pseudo-particles
zbMATH Keywords: Eulerian coordinates
zbMATH Keywords: Lagrangian coordinates
reviewed by: Pavel Burda
MaRDI profile type: Publication
full work available at URL: jcph.1999.6295
OpenAlex ID: W2043260583
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DOI: 10.1006/JCPH.1999.6295
description: scientific article; zbMATH DE number 1384964