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

机译：球壳中具有无限Prandtl数的Rayleigh-Benard方程的稳定有限元方法

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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 Pl/ 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.

机译：针对球壳中具有无限Prandtl数的Boussinesq流体的热对流问题，开发并分析了有限元方案。这个问题是地球地幔运动的数学模型，并且一直是地球物理学家感兴趣的话题。它由具有无限Prandtl数的Rayleigh-Benard方程描述，即由Stokes方程和对流扩散方程以及浮力和对流项组成的系统。提出了具有P1 / P1 / P1单元的稳定有限元方案，并建立了误差估计。数值结果也可以识别出所获得的理论收敛阶数。另一个数值结果显示为地球地幔运动模拟的一个例子。

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《Computer Methods in Applied Mechanics and Engineering》 |2000年第4期|p.387-402|共16页
作者
M. Tabata; A. Suzuki;
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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类自动化基础理论;工程基础科学;
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1. Finite element approximation to infinite Prandtl number Boussinesq equations with temperature-dependent coefficients—Thermal convection problems in a spherical shell [J] . Masahisa Tabata Future generation computer systems . 2006,第4期

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2. Buckling Analyses of Spherical Shells by the Finite Element Method Based on the Willis-Form Equations [J] . International journal of applied mechanics . 2019,第9期

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3. A finite element method for the resolution of the Reduced Navier-Stokes/Prandtl equations [J] . Gabriel R. Barrenechea, Franz Chouly Zeitschrift fur Angewandte Mathematik und Mechanik . 2009,第1期

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4. Finite element approximation to infinite prandtl number boussinesq equations with slip boundary condition [C] . Masahisa Tabata European Computational Fluid Dynamics Conference . 1998

机译：具有滑动边界条件的有限元近似为无限普朗特数Boussinesq方程
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7. 1Three-Dimensional Spherical Shell Convection at Infinite Prandtl Number Using the ‘Cubed Sphere ’ Method [O] . J. W. Hernlunda, P. J. Tackleya 2002

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

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