Front tracking and two-dimensional Riemann problems
type: Item
instance of: scholarly article
title: Front tracking and two-dimensional Riemann problems
zbMATH Open document ID: 0631.76068
DOI: 10.1016/0196-8858(85)90014-4
author: C. Klingenberg
author: James Glimm
author: Oliver A. McBryan
author: B. Plohr
author: David Sharp
author: Sara Yaniv
published in: Advances in Applied Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The so-called method of front tracking is applied to several computation examples of jump discontinuities. Front tracking may be described as follows. A special grid is placed onto the discontinuity and equations are set up to propagate normally and tangentially to the wave front. This approach works away from the points where the discontinuity curves meet. Therefore main interest is drawn to different types of front intersection points described by the introduced new grid variables. Problems under consideration are the regular reflection of shock waves, Mach reflection of shock waves, a classification of two-dimensional elementary waves and conjections concerning Riemann problems. The behaviour of shock waves, contact discontinuities and rarefaction waves at the intersection points is discussed. Results of numerical computation examples are presented. From the mathematical point of view nonlinear hyperbolic systems of partial differential equations are under consideration such as the Euler equations for supersonic flow of a compressible, inviscid, polytropic gas. The mathematical foundations of the method of front tracking, however, one has to take from the literature quoted.
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 4027058
zbMATH Keywords: method of front tracking
zbMATH Keywords: jump discontinuities
zbMATH Keywords: regular reflection of shock waves
zbMATH Keywords: Mach reflection of shock waves
zbMATH Keywords: Riemann problems
zbMATH Keywords: contact discontinuities
zbMATH Keywords: rarefaction waves
zbMATH Keywords: Euler equations
zbMATH Keywords: compressible, inviscid, polytropic gas
reviewed by: J. T. Heynatz
MaRDI profile type: Publication
full work available at URL: 0196-8858(85)90014-4
OpenAlex ID: W4212938577
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cites work: Q5801144
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description: scientific article; zbMATH DE number 4027058