There has been significant progress in the development of numerical geodynamo models over the last five years. Advances in computer technology have made it possible to perform three–dimensional simulations, with thermal or compositional convection as the driving mechanism. These numerical simulations give reasonable results for the morphology and strength of the field at the core–mantle boundary, and the models are also capable of giving reversals and excursions which can be compared with palaeomagnetic observations; they also predict differential rotation between the inner core and the mantle.
However, there are still a number of fundamental problems associated with the simulations, which are proving hard to overcome. Despite the advances in computing power, the models are still expensive and take a long time to run. This problem may diminish as faster machines become available, and new numerical methods exploit parallelization effectively, but currently there are no practical schemes available which work at low Ekman number.
Even with turbulent values of the diffusivities (and the question of whether isotropic diffusivities are appropriate is still unresolved), the appropriate dynamical regime has not yet been reached. In consequence, modelling assumptions about the nature of the flow near the boundaries have to be made, and different choices can have profound effects on the dynamics. The nature of large–scale magnetoconvection at small E is still not well understood, and until we have more understanding of this issue, it will be difficult to have a great deal of confidence in the predictions of the numerical models.