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

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

研究成果: ジャーナルへの寄稿記事

9 引用 (Scopus)

抄録

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.

元の言語英語
ページ(範囲)389-406
ページ数18
ジャーナルNumerische Mathematik
111
発行部数3
DOI
出版物ステータス出版済み - 1 1 2009

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Numerical Verification
Rayleigh
Three-dimensional
Fluids
Computer-assisted Proof
Navier-Stokes Problem
Stream Function
Steady-state Solution
Bifurcation Diagram
Numerical Computation
Convection
Fixed point theorem
Bifurcation
Attack
Fluid
Operator

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

これを引用

A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Bénard problems. / Kim, Myoungnyoun; Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Nishida, Takaaki.

:: Numerische Mathematik, 巻 111, 番号 3, 01.01.2009, p. 389-406.

研究成果: ジャーナルへの寄稿記事

Kim, Myoungnyoun ; Nakao, Mitsuhiro T. ; Watanabe, Yoshitaka ; Nishida, Takaaki. / A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Bénard problems. :: Numerische Mathematik. 2009 ; 巻 111, 番号 3. pp. 389-406.
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