Development of a Simulation Code for MHD Dynamo Processes Using the GeoFEM Platform

Abstract

We have developed a magnetohydrodynamic (MHD) simulation code for a fluid in a rotating spherical shell, modeled on the earth's outer core, using the parallel finite-element method (FEM). This simulation code is designed to elucidate the geodynamo processes and the dynamics of a conductive fluid in the earth's outer core. To connect the magnetic field in the fluid shell and the potential magnetic field in an insulator, a finite element mesh is constructed for the inner core and the mantle as well as for the outer core, and the vector potential of the magnetic field is used to solve for the magnetic field. In the present study, a total of 7.8 × 104 elements are used in the simulation domain. The simulation is performed in 105 time steps spanning 2.5 times the magnetic diffusion time. To reduce the computational time, symmetry with respect to the equatorial plane is assumed. The results show that the magnetic energy generated is approximately four times the kinetic energy. Comparing our results with a spherical harmonics expansion suggests that the approach outlined here gives results equivalent to those of spectral methods, although some discrepancies can be observed. Our simulation code provides the first successful MHD dynamo simulation using the FEM platform.