On Chorin’s Method for Stationary Solutions of the Oberbeck–Boussinesq Equation

Yoshiyuki Kagei, Takaaki Nishida

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Stability of stationary solutions of the Oberbeck–Boussinesq system (OB) and the corresponding artificial compressible system is considered. The latter system is obtained by adding the time derivative of the pressure with small parameter ε> 0 to the continuity equation of (OB), which was proposed by A. Chorin to find stationary solutions of (OB) numerically. Both systems have the same sets of stationary solutions and the system (OB) is obtained from the artificial compressible one as the limit ε→ 0 which is a singular limit. It is proved that if a stationary solution of the artificial compressible system is stable for sufficiently small ε> 0 , then it is also stable as a solution of (OB). The converse is proved provided that the velocity field of the stationary solution satisfies some smallness condition.

Original languageEnglish
Pages (from-to)345-365
Number of pages21
JournalJournal of Mathematical Fluid Mechanics
Volume19
Issue number2
DOIs
Publication statusPublished - Jun 1 2017

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Stationary Solutions
Derivatives
continuity equation
velocity distribution
Singular Limit
Continuity Equation
Converse
Small Parameter
Velocity Field
Derivative

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

Cite this

On Chorin’s Method for Stationary Solutions of the Oberbeck–Boussinesq Equation. / Kagei, Yoshiyuki; Nishida, Takaaki.

In: Journal of Mathematical Fluid Mechanics, Vol. 19, No. 2, 01.06.2017, p. 345-365.

Research output: Contribution to journalArticle

Kagei, Yoshiyuki ; Nishida, Takaaki. / On Chorin’s Method for Stationary Solutions of the Oberbeck–Boussinesq Equation. In: Journal of Mathematical Fluid Mechanics. 2017 ; Vol. 19, No. 2. pp. 345-365.
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