Geodynamo simulations - How realistic are they?

The past seven years have seen significant advances in computational simulations of convection and magnetic field generation in the Earth's core. Although dynamically self-consistent models of the geodynamo have simulated magnetic fields that appear in some ways quite similar to the geomagnetic field, none are able to run in an Earth-like parameter regime because of the considerable spatial resolution that is required. Here we discuss some of the subtle compromises that have been made in current models and propose a grand challenge for the future, requiring significant improvements in numerical methods and spatial resolution.