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H. Kitauchi and S. Kida
Numerical Code for an MHD Simulation in Rotating Spherical Shell
Date of publication:
MHD dynamo, thermal convection, rotating spherical shell, Boussinesq MHD, pseudo-spectral method, Chebyshev tau method, Coupled method, Crank-Nicolson scheme, Adams-Bashforth scheme.
A fast and accurate numerical code is developed which simulates the temporal evolution of thermal convection of an electrically conducting fluid together with induced magnetic field by solving a set of Boussinesq magneto-hydrodynamic (MHD) equations in a rotating spherical shell. This is one of the fundamental models with which the mechanisms of an MHD dynamo in a rotating spherical body such as the Earth is investigated. Spatial variations are described by the use of the spectral method which achieves high numerical accuracy; all the dependent variables are expanded in terms of spherical harmonics on spherical surfaces and Chebyshev polynomials in radial direction. The Chebyshev tau method is employed in order to satisfy boundary conditions. Temporal integration is carried out by the use of the Crank-Nicolson scheme for the viscous term and the second-order Adams-Bashforth scheme for the other terms.
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