Full sphere hydrodynamic and dynamo benchmarks

P. Marti, N. Schaeffer, R. Hollerbach, D. Cebron, 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 journalArticlepeer-review

36 Scopus citations


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. © The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society.
Original languageEnglish (US)
Pages (from-to)119-134
Number of pages16
JournalGeophysical Journal International
Issue number1
StatePublished - Jan 25 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This work was partly funded by ERC grant 247303 ‘MFECE’ to AJ. AJ and PM acknowledge SNF grant 200021-113466, and are grateful for the provision of computational resources by the Swiss National Supercomputing Centre (CSCS) under project ID s225. PM acknowledges the support of the NSF CSEDI Programme through award EAR-1067944. For this work, DC was supported by the ETH Zurich Post-doctoral fellowship programme as well as by the Marie Curie Actions for People COFUND Programme. JLG acknowledges support from the University Paris-Sud, the National Science Foundation (grants NSF DMS-1015984 and DMS-1217262), the Air Force Office of Scientific Research, (grant FA99550-12-0358) and the King Abdullah University of Science and Technology (Award No. KUS-C1-016-04). The computations using SFEMaNS were carried out on IBM SP6 of GENCI-IDRIS (project 0254).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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