Full sphere hydrodynamic and dynamo benchmarks

P. Marti, N. Schaeffer, R. Hollerbach, D. Cébron, C. Nore, F. Luddens, J. L. Guermond, J. Aubert, S. Takehiro, Y. Sasaki, Y. Y. Hayashi, R. Simitev, F. Busse, S. Vantieghem, A. Jackson

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

Convection in planetary cores can generate fluid flow and magnetic fields, and a number of sophisticated codes exist to simulate the dynamic behaviour of such systems. We report on the first community activity to compare numerical results of computer codes designed to calculate fluid flow within a whole sphere. The flows are incompressible and rapidly rotating and the forcing of the flow is either due to thermal convection or due to moving boundaries. All problems defined have solutions that alloweasy comparison, since they are either steady, slowly drifting or perfectly periodic. The first two benchmarks are defined based on uniform internal heating within the sphere under the Boussinesq approximation with boundary conditions that are uniform in temperature and stress-free for the flow. Benchmark 1 is purely hydrodynamic, and has a drifting solution. Benchmark 2 is a magnetohydrodynamic benchmark that can generate oscillatory, purely periodic, flows and magnetic fields. In contrast, Benchmark 3 is a hydrodynamic rotating bubble benchmark using no slip boundary conditions that has a stationary solution. Results from a variety of types of code are reported, including codes that are fully spectral (based on spherical harmonic expansions in angular coordinates and polynomial expansions in radius), mixed spectral and finite difference, finite volume, finite element and also a mixed Fourier-finite element code. There is good agreement between codes. It is found that in Benchmarks 1 and 2, the approximation of a whole sphere problem by a domain that is a spherical shell (a sphere possessing an inner core) does not represent an adequate approximation to the system, since the results differ from whole sphere results.

Original languageEnglish
Pages (from-to)119-134
Number of pages16
JournalGeophysical Journal International
Volume197
Issue number1
Early online date25 Jan 2014
DOIs
Publication statusPublished - Apr 2014
Externally publishedYes

Fingerprint

Hydrodynamics
hydrodynamics
fluid flow
Flow of fluids
Flow fields
flow distribution
flow field
planetary cores
Boundary conditions
boundary conditions
Magnetic fields
boundary condition
Boussinesq approximation
core (planetary)
expansion
incompressible flow
Incompressible flow
magnetic field
spherical shells
spherical harmonics

Keywords

  • Dynamo:theories and simulations
  • Non-linear differential equations
  • Numerical solutions
  • Planetary interiors

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics

Cite this

Marti, P., Schaeffer, N., Hollerbach, R., Cébron, D., Nore, C., Luddens, F., ... Jackson, A. (2014). Full sphere hydrodynamic and dynamo benchmarks. Geophysical Journal International, 197(1), 119-134. https://doi.org/10.1093/gji/ggt518

Full sphere hydrodynamic and dynamo benchmarks. / Marti, P.; Schaeffer, N.; Hollerbach, R.; Cébron, D.; Nore, C.; Luddens, F.; Guermond, J. L.; Aubert, J.; Takehiro, S.; Sasaki, Y.; Hayashi, Y. Y.; Simitev, R.; Busse, F.; Vantieghem, S.; Jackson, A.

In: Geophysical Journal International, Vol. 197, No. 1, 04.2014, p. 119-134.

Research output: Contribution to journalArticle

Marti, P, Schaeffer, N, Hollerbach, R, Cébron, D, Nore, C, Luddens, F, Guermond, JL, Aubert, J, Takehiro, S, Sasaki, Y, Hayashi, YY, Simitev, R, Busse, F, Vantieghem, S & Jackson, A 2014, 'Full sphere hydrodynamic and dynamo benchmarks' Geophysical Journal International, vol. 197, no. 1, pp. 119-134. https://doi.org/10.1093/gji/ggt518
Marti P, Schaeffer N, Hollerbach R, Cébron D, Nore C, Luddens F et al. Full sphere hydrodynamic and dynamo benchmarks. Geophysical Journal International. 2014 Apr;197(1):119-134. https://doi.org/10.1093/gji/ggt518
Marti, P. ; Schaeffer, N. ; Hollerbach, R. ; Cébron, D. ; Nore, C. ; Luddens, F. ; Guermond, J. L. ; Aubert, J. ; Takehiro, S. ; Sasaki, Y. ; Hayashi, Y. Y. ; Simitev, R. ; Busse, F. ; Vantieghem, S. ; Jackson, A. / Full sphere hydrodynamic and dynamo benchmarks. In: Geophysical Journal International. 2014 ; Vol. 197, No. 1. pp. 119-134.
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