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| Titel |
On the sensitivity of 3-D thermal convection codes to numerical discretization: a model intercomparison |
| VerfasserIn |
P.-A. Arrial, N. Flyer, G. B. Wright, L. H. Kellogg |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1991-959X
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| Digitales Dokument |
URL |
| Erschienen |
In: Geoscientific Model Development ; 7, no. 5 ; Nr. 7, no. 5 (2014-09-15), S.2065-2076 |
| Datensatznummer |
250115721
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| Publikation (Nr.) |
 copernicus.org/gmd-7-2065-2014.pdf |
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| Zusammenfassung |
| Fully 3-D numerical simulations of thermal convection in a spherical shell
have become a standard for studying the dynamics of pattern formation and its
stability under perturbations to various parameter values. The question
arises as to how the discretization of the governing equations affects the
outcome and thus any physical interpretation. This work demonstrates the
impact of numerical discretization on the observed patterns, the value at
which symmetry is broken, and how stability and stationary behavior is
dependent upon it. Motivated by numerical simulations of convection in the
Earth's mantle, we consider isoviscous Rayleigh–Bénard convection at
infinite Prandtl number, where the aspect ratio between the inner and outer
shell is 0.55. We show that the subtleties involved in developing mantle
convection models are considerably more delicate than has been previously
appreciated, due to the rich dynamical behavior of the system. Two codes with
different numerical discretization schemes – an established,
community-developed, and benchmarked finite-element code (CitcomS) and a
novel spectral method that combines Chebyshev polynomials with radial basis
functions (RBFs) – are compared. A full numerical study is investigated for
the following three cases. The first case is based on the cubic (or
octahedral) initial condition (spherical harmonics of degree ℓ = 4). How
this pattern varies to perturbations in the initial condition and Rayleigh
number is studied. The second case investigates the stability of the
dodecahedral (or icosahedral) initial condition (spherical harmonics of
degree ℓ = 6). Although both methods first converge to the same pattern,
this structure is ultimately unstable and systematically degenerates to cubic
or tetrahedral symmetries, depending on the code used. Lastly, a new
steady-state pattern is presented as a combination of third- and fourth-order
spherical harmonics leading to a five-cell or hexahedral pattern and stable
up to 70 times the critical Rayleigh number. This pattern can provide the
basis for a new accuracy benchmark for 3-D spherical mantle convection codes. |
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