### Abstract

As high-performance computing facilities and sophisticated modeling software become available, modeling mantle convection in a three-dimensional (3-D) spherical shell geometry with realistic physical parameters and processes becomes increasingly feasible. However, there is still a lack of comprehensive benchmark studies for 3-D spherical mantle convection. Here we present benchmark and test calculations using a finite element code CitcomS for 3-D spherical convection. Two classes of model calculations are presented: the Stokes' flow and thermal and thermochemical convection. For Stokes' flow, response functions of characteristic flow velocity, topography, and geoid at the surface and core-mantle boundary (CMB) at different spherical harmonic degrees are computed using CitcomS and are compared with those from analytic solutions using a propagator matrix method. For thermal and thermochemical convection, 24 cases are computed with different model parameters including Rayleigh number (7 × 10^{3} or 10^{5}) and viscosity contrast due to temperature dependence (1 to 10^{7}). For each case, time-averaged quantities at the steady state are computed, including surface and CMB Nussult numbers, RMS velocity, averaged temperature, and maximum and minimum flow velocity, and temperature at the midmantle depth and their standard deviations. For thermochemical convection cases, in addition to outputs for thermal convection, we also quantified entrainment of an initially dense component of the convection and the relative errors in conserving its volume. For nine thermal convection cases that have small viscosity variations and where previously published results were available, we find that the CitcomS results are mostly consistent with these previously published with less than 1% relative differences in globally averaged quantities including Nussult numbers and RMS velocities. For other 15 cases with either strongly temperature-dependent viscosity or thermochemical convection, no previous calculations are available for comparison, but these 15 test calculations from CitcomS are useful for future code developments and comparisons. We also presented results for parallel efficiency for CitcomS, showing that the code achieves 57% efficiency with 3072 cores on Texas Advanced Computing Center's parallel supercomputer Ranger.

Original language | English (US) |
---|---|

Article number | Q10017 |

Journal | Geochemistry, Geophysics, Geosystems |

Volume | 9 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2008 |

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### Keywords

- Benchmark
- Mantle convection

### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics

### Cite this

*Geochemistry, Geophysics, Geosystems*,

*9*(10), [Q10017]. https://doi.org/10.1029/2008GC002048

**A benchmark study on mantle convection in a 3-D spherical shell using CitcomS.** / Zhong, Shijie; McNamara, Allen; Tan, Eh; Moresi, Louis; Gurnis, Michael.

Research output: Contribution to journal › Article

*Geochemistry, Geophysics, Geosystems*, vol. 9, no. 10, Q10017. https://doi.org/10.1029/2008GC002048

}

TY - JOUR

T1 - A benchmark study on mantle convection in a 3-D spherical shell using CitcomS

AU - Zhong, Shijie

AU - McNamara, Allen

AU - Tan, Eh

AU - Moresi, Louis

AU - Gurnis, Michael

PY - 2008/10

Y1 - 2008/10

N2 - As high-performance computing facilities and sophisticated modeling software become available, modeling mantle convection in a three-dimensional (3-D) spherical shell geometry with realistic physical parameters and processes becomes increasingly feasible. However, there is still a lack of comprehensive benchmark studies for 3-D spherical mantle convection. Here we present benchmark and test calculations using a finite element code CitcomS for 3-D spherical convection. Two classes of model calculations are presented: the Stokes' flow and thermal and thermochemical convection. For Stokes' flow, response functions of characteristic flow velocity, topography, and geoid at the surface and core-mantle boundary (CMB) at different spherical harmonic degrees are computed using CitcomS and are compared with those from analytic solutions using a propagator matrix method. For thermal and thermochemical convection, 24 cases are computed with different model parameters including Rayleigh number (7 × 103 or 105) and viscosity contrast due to temperature dependence (1 to 107). For each case, time-averaged quantities at the steady state are computed, including surface and CMB Nussult numbers, RMS velocity, averaged temperature, and maximum and minimum flow velocity, and temperature at the midmantle depth and their standard deviations. For thermochemical convection cases, in addition to outputs for thermal convection, we also quantified entrainment of an initially dense component of the convection and the relative errors in conserving its volume. For nine thermal convection cases that have small viscosity variations and where previously published results were available, we find that the CitcomS results are mostly consistent with these previously published with less than 1% relative differences in globally averaged quantities including Nussult numbers and RMS velocities. For other 15 cases with either strongly temperature-dependent viscosity or thermochemical convection, no previous calculations are available for comparison, but these 15 test calculations from CitcomS are useful for future code developments and comparisons. We also presented results for parallel efficiency for CitcomS, showing that the code achieves 57% efficiency with 3072 cores on Texas Advanced Computing Center's parallel supercomputer Ranger.

AB - As high-performance computing facilities and sophisticated modeling software become available, modeling mantle convection in a three-dimensional (3-D) spherical shell geometry with realistic physical parameters and processes becomes increasingly feasible. However, there is still a lack of comprehensive benchmark studies for 3-D spherical mantle convection. Here we present benchmark and test calculations using a finite element code CitcomS for 3-D spherical convection. Two classes of model calculations are presented: the Stokes' flow and thermal and thermochemical convection. For Stokes' flow, response functions of characteristic flow velocity, topography, and geoid at the surface and core-mantle boundary (CMB) at different spherical harmonic degrees are computed using CitcomS and are compared with those from analytic solutions using a propagator matrix method. For thermal and thermochemical convection, 24 cases are computed with different model parameters including Rayleigh number (7 × 103 or 105) and viscosity contrast due to temperature dependence (1 to 107). For each case, time-averaged quantities at the steady state are computed, including surface and CMB Nussult numbers, RMS velocity, averaged temperature, and maximum and minimum flow velocity, and temperature at the midmantle depth and their standard deviations. For thermochemical convection cases, in addition to outputs for thermal convection, we also quantified entrainment of an initially dense component of the convection and the relative errors in conserving its volume. For nine thermal convection cases that have small viscosity variations and where previously published results were available, we find that the CitcomS results are mostly consistent with these previously published with less than 1% relative differences in globally averaged quantities including Nussult numbers and RMS velocities. For other 15 cases with either strongly temperature-dependent viscosity or thermochemical convection, no previous calculations are available for comparison, but these 15 test calculations from CitcomS are useful for future code developments and comparisons. We also presented results for parallel efficiency for CitcomS, showing that the code achieves 57% efficiency with 3072 cores on Texas Advanced Computing Center's parallel supercomputer Ranger.

KW - Benchmark

KW - Mantle convection

UR - http://www.scopus.com/inward/record.url?scp=70350654855&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350654855&partnerID=8YFLogxK

U2 - 10.1029/2008GC002048

DO - 10.1029/2008GC002048

M3 - Article

VL - 9

JO - Geochemistry, Geophysics, Geosystems

JF - Geochemistry, Geophysics, Geosystems

SN - 1525-2027

IS - 10

M1 - Q10017

ER -