Thermal convection analysis in a rotating shell by a parallel finite-element method—development of a thermal-hydraulic subsystem of GeoFEM

摘要

The purpose of this paper is to propose a method for the numerical simulation of thermally driven convection in a rotating spherical shell modeled on the Earth's outer core using the GeoFEM thermal-hydraulic subsystem, which provides a parallel finite-element method (FEM) platform. This simulation is designed to assist in the understanding of the origin of the geomagnetic field and the dynamics of the fluid in the Earth's outer core. A three-dimensional and time-dependent process of a Boussinesq fluid in a rotating spherical shell is solved under the effects of self-gravity and the Coriolis force. A tri-linear hexahedral element is used for the spatial distribution. A total of 1.26 x 10~5 nodes were used on the spherical shell, and the finite-element mesh was divided into 32 domains for parallel computation. The second-order Adams-Bashforth scheme was used for the time integration of temperature and velocity. To satisfy mass conservation, a parallel iterative solver given by GeoFEM was used to solve for the pressure and correction of the velocity fields, and the simulation was performed over 10~5 steps using four nodes of a Hitachi SR8000. To verify the proposed simulation code, results of the simulation are compared with analysis by the spectral method. The results show that the outline of convection is approximately equal; that is, three pairs of convection columns are formed, and these columns propagate westward in a quasi-steady state. However, the magnitude of kinetic energy averaged over the shell is approximately 93 % of that by the spectral method, and the drift frequency of the columns in the GeoFEM simulation is larger than that by the spectral method.