On initial-value and self-similar solutions of the compressible Euler equations

Ravindra Samtaney*, D. I. Pullin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

62 Scopus citations

Abstract

We examine numerically the issue of convergence for initial-value solutions and similarity solutions of the compressible Euler equations in two dimensions in the presence of vortex sheets (slip lines). We consider the problem of a normal shock wave impacting an inclined density discontinuity in the presence of a solid boundary. Two solution techniques are examined: the first solves the Euler equations by a Godunov method as an initial-value problem and the second as a boundary value problem, after invoking self-similarity. Our results indicate nonconvergence of the initial-value calculation at fixed time, with increasing spatial-temporal resolution. The similarity solution appears to converge to the weak 'zero-temperature' solution of the Euler equations in the presence of the slip line. Some speculations on the geometric character of solutions of the initial-value problem are presented.

Original languageEnglish (US)
Pages (from-to)2650-2655
Number of pages6
JournalPhysics of Fluids
Volume8
Issue number10
DOIs
StatePublished - Jan 1 1996

ASJC Scopus subject areas

  • Condensed Matter Physics

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