A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Bénard problems

Myoungnyoun Kim, Mitsuhiro T. Nakao, Yoshitaka Watanabe, Takaaki Nishida

    Research output: Contribution to journalArticlepeer-review

    9 Citations (Scopus)

    Abstract

    This paper is the three dimensional extension of the two dimensional work in Nakao et al. (Reliable Comput 9(5):359-372, 2003) and Watanabe et al. (J Math Fluid Mech 6:1-20, 2004) on a computer assisted proof of the existence of nontrivial steady state solutions for Rayleigh-Bénard convection based on the fixed point theorem using a Newton like operator. The differences are emerging of complicated types of bifurcation, direct attack on the problem without stream functions, and increased complexity of numerical computation. The last one makes it hard to proceed the verification of solutions corresponding to the points on bifurcation diagram for three dimensional case. Actually, this work should be the first result for the three dimensional Navier-Stokes problems which seems to be very difficult to solve by theoretical approaches.

    Original languageEnglish
    Pages (from-to)389-406
    Number of pages18
    JournalNumerische Mathematik
    Volume111
    Issue number3
    DOIs
    Publication statusPublished - Jan 2009

    All Science Journal Classification (ASJC) codes

    • Computational Mathematics
    • Applied Mathematics

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