Perhaps the geomagnetic field is best understood in terms of a self-exciting
dynamo model? Topological differences (e.g., the hole), however, and
symmetry considerations render it unlikely that the geodynamo is like a
self-exciting disk dynamo.
Regardless, magnetohydrodynamic calculations are exceeding difficult. A
fair start on this topic can be obtained from a review of C.M.R. Fowler's
excellent text -- The Solid Earth (University of Cambridge Press,
ISBN0-521-38590-3).
Although I don't know his present status, for the email ambitious, I
believe that Dr.. Fowler used to be at the University of Saskatchewan.