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

Yoshitaka Watanabe, Michael Plum, Mitsuhiro T. Nakao

    Research output: Contribution to journalArticlepeer-review

    14 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 2008

    All Science Journal Classification (ASJC) codes

    • Computational Mechanics
    • Applied Mathematics

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