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

M. Tabata, A. Suzuki

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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

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ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics

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