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@article{CHRISTENSEN200125,
title = "A numerical dynamo benchmark",
journal = "Physics of the Earth and Planetary Interiors",
volume = "128",
number = "1",
pages = "25 - 34",
year = "2001",
note = "Dynamics and Magnetic Fields of the Earth's and Planetary Interiors",
issn = "0031-9201",
doi = "https://doi.org/10.1016/S0031-9201(01)00275-8",
url = "http://www.sciencedirect.com/science/article/pii/S0031920101002758",
author = "U.R. Christensen and J. Aubert and P. Cardin and E. Dormy and S. Gibbons and G.A. Glatzmaier and E. Grote and Y. Honkura and C. Jones and M. Kono and M. Matsushima and A. Sakuraba and F. Takahashi and A. Tilgner and J. Wicht and K. Zhang",
keywords = "Geodynamo, Numerical modeling",
abstract = "We present the results of a benchmark study for a convection-driven magnetohydrodynamic dynamo problem in a rotating spherical shell. The solutions are stationary aside from azimuthal drift. One case of non-magnetic convection and two dynamos that differ in the assumptions concerning the inner core are studied. Six groups contributed numerical solutions which show good agreement. This provides an accurate reference standard with high confidence."
}

@article{GLATZMAIER1984461,
title = "Numerical simulations of stellar convective dynamos. I. the model and method",
journal = "Journal of Computational Physics",
volume = "55",
number = "3",
pages = "461 - 484",
year = "1984",
issn = "0021-9991",
doi = "https://doi.org/10.1016/0021-9991(84)90033-0",
url = "http://www.sciencedirect.com/science/article/pii/0021999184900330",
author = "Gary A Glatzmaier",
abstract = "A numerical model used to simulate global convection and magnetic field generation in stars is described. Nonlinear, three-dimensional, time-dependent solutions of the anelastic magnetohydrodynamic equations are presented for a stratified, rotating, spherical, fluid shell heated from below. The velocity, magnetic field, and thermodynamic perturbations are expanded in spherical harmonics to resolve their horizontal structure and in Chebyshev polynomials to resolve their radial structure. An explicit Adams-Bashforth time integration scheme is used with an implicit Crank-Nicolson treatment of the diffusion terms. Nonlinear terms are computed in physical space; and spatial derivatives are computed in spectral space. The resulting second-order differential equations are solved with a Chebyshev collocation method. Preliminary solutions for a Solar-like model are briefly discussed. Convective motions driven in the upper, superadiabatic part of the zone penetrate into the lower, subadiabatic part of the zone. Differential rotation, induced by the interaction of convection and rotation, is an equatorial acceleration at the surface as observed on the Sun; below the surface angular velocity decreases with depth. The meridional circulation and the equator-pole temperature excess are within Solar observational constraints; however, the giant-cell velocities at the surface are larger than observed. The large-scale magnetic field, induced by the differential rotation and helical motions, peaks in the subadiabatic region below the convection zone; and, near the top of the convection zone, it is concentrated over the downdrafts of giant cells. A systematic drift in latitude of the magnetic field or a field reversal has not yet been seen."
}

@article{Glatzmaier1999,
 author = {Glatzmaier, G. A. and Clune, T. C. and Elliott, J. R. and Miesch, M. S. and Toomre, J.},
 title = {Computational Aspects of a Code to Study Rotating Turbulent Convection in Spherical Shells},
 journal = {Parallel Comput.},
 issue_date = {April 1999},
 volume = {25},
 number = {4},
 month = apr,
 year = {1999},
 issn = {0167-8191},
 pages = {361--380},
 numpages = {20},
 url = {http://dx.doi.org/10.1016/S0167-8191(99)00009-5},
 doi = {10.1016/S0167-8191(99)00009-5},
 acmid = {315009},
 publisher = {Elsevier Science Publishers B. V.},
 address = {Amsterdam, The Netherlands, The Netherlands},
 keywords = {anelastic spherical harmonic code, convection},
}

@Article{Heimpel_etal2016,
  author="Heimpel, M.
  and Gastine, T.
  and Wicht, J.",
  title="Simulation of deep-seated zonal jets and shallow vortices in gas giant atmospheres",
  journal="Nature Geoscience",
  year="2016",
  volume="9",
  pages="19-23",
  doi="10.1038/ngeo2601",
  opturl="https://doi.org/10.1038/ngeo2601"
}

@article{JONES2011120,
title = "Anelastic convection-driven dynamo benchmarks",
journal = "Icarus",
volume = "216",
number = "1",
pages = "120 - 135",
year = "2011",
issn = "0019-1035",
doi = "https://doi.org/10.1016/j.icarus.2011.08.014",
url = "http://www.sciencedirect.com/science/article/pii/S0019103511003319",
author = "C.A. Jones and P. Boronski and A.S. Brun and G.A. Glatzmaier and T. Gastine and M.S. Miesch and J. Wicht",
keywords = "Magnetic fields, Jovian planets, Interiors",
abstract = "Benchmark solutions for fully nonlinear anelastic compressible convection and dynamo action in a rotating spherical shell are proposed. Three benchmarks are specified. The first is a purely hydrodynamic case, which is steady in a uniformly drifting frame. The second is a self-excited saturated dynamo solution, also steady in a drifting frame. The third is again a self-excited dynamo but is unsteady in time, and it has a higher Rayleigh number than the steady dynamo benchmark. Four independent codes have been tested against these benchmarks, and very satisfactory agreement has been found. This provides an accurate reference standard against which new anelastic codes can be tested."
}
