A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow

Yoshitaka Watanabe, Michael Plum, Mitsuhiro T. Nakao

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13 Citations (Scopus)

Abstract

This paper presents a computer-assisted proof of solutions of the Orr-Sommerfeld equation describing hydrodynamic stability of Poiseuille flow. A numerical verification method for computing eigenpair enclosures for this non-selfadjoint eigenvalue problem is described. Some verification results confirm the effectiveness of the method. This constitutes the first strict mathematical instability proof for the Poiseuille flow.

Original languageEnglish
Pages (from-to)5-18
Number of pages14
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume89
Issue number1
DOIs
Publication statusPublished - Jan 1 2008

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All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Applied Mathematics

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