Stabilized finite element method for the Rayleigh-Benard equations with infinite Prandtl number in a spherical shell

M. Tabata, A. Suzuki

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

A finite element scheme is developed and analyzed for a thermal convection problem of Boussinesq fluid with infinite Prandtl number in a spherical shell. This problem is a mathematical model of the Earth's mantle movement and has been a topic of interest for geophysicists. It is described by the Rayleigh-Benard equations with infinite Prandtl number, that is, a system of the Stokes equations and the convection-diffusion equation coupled with the buoyancy and the convection terms. A stabilized finite element scheme with P1/P1/P1 element is presented, and an error estimate is established. The obtained theoretical convergence order is also recognized by a numerical result. Another numerical result is shown as an example of the Earth's mantle movement simulation.

Original languageEnglish
Pages (from-to)387-402
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Volume190
Issue number3-4
Publication statusPublished - 2000 Oct 27
Externally publishedYes

Fingerprint

spherical shells
Prandtl number
finite element method
Earth mantle
convection-diffusion equation
Finite element method
Earth (planet)
buoyancy
free convection
mathematical models
convection
Buoyancy
fluids
estimates
Mathematical models
Fluids
simulation
Convection

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics

Cite this

Stabilized finite element method for the Rayleigh-Benard equations with infinite Prandtl number in a spherical shell. / Tabata, M.; Suzuki, A.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 190, No. 3-4, 27.10.2000, p. 387-402.

Research output: Contribution to journalArticle

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