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A New Numerical Scheme in the Solution of the Geodynamo Z-Model

Published online by Cambridge University Press:  19 July 2016

Pavel Hejda  and
Alexander P. Anufrijev
Pavel Hejda
Affiliation:
Geophysical Institute, 141 31 Prague 4, Czechoslovakia
Alexander P. Anufrijev
Affiliation:
Geophysical Institute, Sofia, Bulgaria

Abstract

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The hydromagnetic dynamo Z-model represents a nonlinear dynamic system. Its steady-state solution is derived by step-by-step integration of parabolic partial differential equations of the second order with the use of the finite difference method. Until now, two methods have been used: the semi-implicit method in which the θ-diffusion was carried out implicitly while the r-diffusion explicitly, and the implicit method in which the complete diffusion was carried out implicitly. In the present contribution, a combined semi-implicit method is suggested which reflects not only the singularity at the coordinate system origin but also the decreasing mesh size near the core-mantle boundary. This procedure preserves the advantage of semi-implicit methods and, simultaneously, increases the stability in the most critical boundary layer.

Type
10. Geodynamo and Planetary Dynamos
Information
Symposium - International Astronomical Union , Volume 157: The Cosmic Dynamo , 1993 , pp. 441 - 445
Copyright
Copyright © Kluwer 1993 

References

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