Keywords
discretization
spherical shell
geodynamo
How to Cite
Abstract
this paper presents a conservative finite-difference scheme for the magnetic induction equation in spherical coordinates. We based the approach on the integral form of Faraday’s law of induction applied to the faces of control volumes. We performed the discretization with the finite volume method using a fully implicit scheme and constrained transport (CT). We derived the grid metric terms and the coefficients of the discrete form of the magnetic induction equation in spherical coordinates. We analyzed a special case of approximating the radial component of the electric field at control-volume edges located on the polar axis (θ = 0,π). We implemented the resulting numerical scheme in the CVMHD code developed by the authors for simulations of magnetohydrodynamic flows and hydromagnetic dynamo in spherical shells.
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