A finite-volume solution method for thermal convection and dynamo problems in spherical shells

SUMMARY We present a novel application of a finite-volume technique to the numerical simulation of thermal convection within a rapidly rotating spherical shell. The performance of the method is extensively tested against a known standard solution at moderate Ekman number. Models at lower Ekman number demonstrate the potential of the method in a parameter range more appropriate to the flow in the molten metallic core of planetary interiors. In addition we present results for the magnetohydrodynamic dynamo problem. In order to avoid the need to solve for the magnetic field in the exterior, we use an approximate magnetic boundary condition. Compared with the geophysically relevant case of insulating boundaries, it is shown that the qualitative structures of the flow and the magnetic field are similar. However, a more quantitative comparison indicates that mean flow velocity and mean magnetic field strength are affected by the boundary conditions by about 20 per cent.

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