Full sphere hydrodynamic and dynamo benchmarks

Marti, P. et al. (2014) Full sphere hydrodynamic and dynamo benchmarks. Geophysical Journal International, 197(1), pp. 119-134. (doi:10.1093/gji/ggt518)

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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 allow easy 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.

Item Type:Articles
Additional Information:This is an electronic version of an article published in Geophysical Journal International 197(1):119-134 Copyright © 2014 The Authors. Published by Oxford University Press on behalf of The Royal Astronomical Society. All rights reserved.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Simitev, Dr Radostin
Authors: Marti, P., Schaeffer, N., Hollerbach, R., Cebron, D., Nore, C., Luddens, F., Guermond, J.L., Aubert, J., Takehiro, S., Sasaki, Y., Hayashi, Y., Simitev, R., Busse, F.H., Vantieghem, S., and Jackson, A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Geophysical Journal International
Publisher:Oxford University Press
ISSN:0956-540X
ISSN (Online):1365-246X
Copyright Holders:Copyright © 2014 The Authors
First Published:First published in Geophysical Journal International 197(1):119-134
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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