Application of high order compact finite difference algorithms on non-uniform grids to numerical geodynamo simulation

The Earth possesses a magnetic field of internal origin (core geomagnetic field) in much of its history. This field is generated and maintained by convective flow in the Earth's liquid outer core (geodynamo). Currently several numerical models have been successfully developed with various algorithms to model the dynamo process. Among them include the mixed approach of applying spectral algorithms on spherical surfaces and finite difference algorithms in radius. In our study, we focus on examining the applicability of high (6th and 8th) order, compact finite difference algorithms with non-uniform radial grids to numerical geodynamo modeling. The non-uniform radial grids are used to resolve thin boundary layers at the core-mantle boundary (CMB) and at the inner core boundary (ICB). We are in particular interested in the effect of the algorithms on nonlinear couplings among the magnetic field, the velocity field and the density perturbations. The results are used to compare those from our MoSST core dynamics model which employs a 4th order finite difference algorithm in radius.