### Abstract

A finite element code is developed for a thermal convection problem of infinite Prandtl number Boussinesq fluid subject to slip velocity boundary conditions. The problem is a fundamental mathematical model of the Earth's mantle movement. It is described by a couple of the Stokes equations and the convection-diffusion equation combined by buoyancy and convection terms. A stabilized finite element scheme with P1/P1/P1 element is employed. Some numerical computations in a three-dimensional spherical shell with Rayleigh number 10
^{4} are performed. Time histories of the Nusselt numbers and the root-mean-square velocities are computed, which are observed to be convergent as the mesh subdivisions become finer.

Original language | English |
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Title of host publication | Theoretical and Applied Mechanics |

Pages | 371-378 |

Number of pages | 8 |

Volume | 48 |

Publication status | Published - 1999 |

Externally published | Yes |

Event | Proceedings of the 1999 48th Japan National Congress on Theoretical and Applied Mechanics (NCTAM) - Tokyo, Jpn Duration: 1999 Jan 25 → 1999 Jan 27 |

### Other

Other | Proceedings of the 1999 48th Japan National Congress on Theoretical and Applied Mechanics (NCTAM) |
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City | Tokyo, Jpn |

Period | 99/1/25 → 99/1/27 |

### Fingerprint

### ASJC Scopus subject areas

- Mechanics of Materials

### Cite this

*Theoretical and Applied Mechanics*(Vol. 48, pp. 371-378)

**Numerical solution of an unsteady Earth's mantle convection problem by a stabilized finite element method.** / Suzuki, Atsushi; Tabata, Masahisa; Honda, Satoru.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Theoretical and Applied Mechanics.*vol. 48, pp. 371-378, Proceedings of the 1999 48th Japan National Congress on Theoretical and Applied Mechanics (NCTAM), Tokyo, Jpn, 99/1/25.

}

TY - GEN

T1 - Numerical solution of an unsteady Earth's mantle convection problem by a stabilized finite element method

AU - Suzuki, Atsushi

AU - Tabata, Masahisa

AU - Honda, Satoru

PY - 1999

Y1 - 1999

N2 - A finite element code is developed for a thermal convection problem of infinite Prandtl number Boussinesq fluid subject to slip velocity boundary conditions. The problem is a fundamental mathematical model of the Earth's mantle movement. It is described by a couple of the Stokes equations and the convection-diffusion equation combined by buoyancy and convection terms. A stabilized finite element scheme with P1/P1/P1 element is employed. Some numerical computations in a three-dimensional spherical shell with Rayleigh number 10 4 are performed. Time histories of the Nusselt numbers and the root-mean-square velocities are computed, which are observed to be convergent as the mesh subdivisions become finer.

AB - A finite element code is developed for a thermal convection problem of infinite Prandtl number Boussinesq fluid subject to slip velocity boundary conditions. The problem is a fundamental mathematical model of the Earth's mantle movement. It is described by a couple of the Stokes equations and the convection-diffusion equation combined by buoyancy and convection terms. A stabilized finite element scheme with P1/P1/P1 element is employed. Some numerical computations in a three-dimensional spherical shell with Rayleigh number 10 4 are performed. Time histories of the Nusselt numbers and the root-mean-square velocities are computed, which are observed to be convergent as the mesh subdivisions become finer.

UR - http://www.scopus.com/inward/record.url?scp=0033311142&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033311142&partnerID=8YFLogxK

M3 - Conference contribution

VL - 48

SP - 371

EP - 378

BT - Theoretical and Applied Mechanics

ER -