Exact solutions of compressible plane potential flows - a new approach
type: Item
instance of: scholarly article
title: Exact solutions of compressible plane potential flows - a new approach
zbMATH Open document ID: 0887.76062
author: O. Diekmann
published in: Archive for Rational Mechanics and Analysis
publication date: 1998-04-28T00:00:00Z
review text: The paper presents a new method for finding exact closed-form solutions of steady plane irrotational flow of compressible fluids when the pressure is a single-valued function of density only. A short description of two existing methods for finding exact solution can be found in the introduction. The authors' method is based on introducing a streamfunction \(\psi\) and then on treatment the plane variables \(x,y\), velocities \(u,v\), pressure \(p\) and density \(\rho\) as functions of \(\beta, \psi\) instead of independent variables \(x,y.\) Here \(\beta,\psi\) form curvilinear coordinates in the physical plane in which the curves \(\psi=\)const are the streamlines. It is shown that this approach delivers infinitely many solutions for the full potential equation. Vortex and spiral flows are re-discovered, too.
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 1045413
zbMATH Keywords: streamfunction
zbMATH Keywords: spiral flows
zbMATH Keywords: vortex flow
reviewed by: P. B. Dubovski
MaRDI profile type: Publication
full work available at URL: s002050050027
OpenAlex ID: W2007371351
DOI: 10.1007/S002050050027
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description: scientific article; zbMATH DE number 1045413