## New Geodynamo and Mantle Convection Simulation Results from the Earth Simulator Using the Yin-Yang Grid

### Akira Kageyama and Masaki Yoshida, JAMSTEC

Since the Earth is composed of spherical layers, computer simulations of the Earth's interior need efficient spatial discretization methods in the spherical shell geometry.  Recently, a new spherical grid system, the "Yin-Yang grid," has been developed for geophysical simulations.  Because there is no grid mesh that is orthogonal over the entire spherical surface and, at the same time, free of coordinate singularity or grid convergence, we have chosen an overset grid approach.  Specifically, a spherical surface is decomposed into two identical subregions. The decomposition (or dissection) enables us to cover each subregion by a grid system that is individually orthogonal and singularity-free.  Each component grid in this Yin-Yang grid is a low latitude component of the usual latitude-longitude grid on the spherical polar coordinates (90 degree about the equator and 270 degree in the longitude).  Therefore, the grid spacing is quasi-uniform and metric tensors are simple and analytically known.  One can directly apply mathematical and numerical resources that have been written in the spherical polar coordinates or latitude-longitude grid.  Since the two component grids are identical and they are combined in a complementary way, various routines of the code can be recycled twice for each component grid at every simulation time step.  We have developed finite difference codes based on the Yin-Yang grid for (i) the geodynamo simulation, and (ii) the mantle convection simulation. In the geodynamo simulation, we calculate the temporal evolution of thermal convection of an electrically conducting fluid in a rotating spherical shell (outer core).  In the mantle convection simulation, we calculate the time development of thermal convection motion of a Boussinesq fluid with infinite Prandtl number in a spherical shell (mantle).  The intrinsic simplicity of the mesh configuration of the Yin-Yang grid enables us to develop highly optimized simulation codes on a massively parallel supercomputer such as the Earth Simulator (ES).  The Yin-Yang Geodynamo Code has now achieved 15.6 Tflops with 4096 processors on the ES.  This represents 46% of the theoretical peak performance.  Compared with previous studies, the Yin-Yang grid has enabled performing mantle convection and geodynamo simulations in more realistic regimes.  For example, we can now carry out calculations with a Rayleigh number of 10^7, which is close to the real value of the Earth's mantle, including strongly temperature-dependent viscosity that is also an essential feature of the real mantle.  When the viscosity contrast across the mantle layer is greater than 10^5, a characteristic convection pattern with a cold and stiff layer (so-called "stagnant-lid'') emerges on the Earth's surface that can be compared with the lithosphere.  The present Yin-Yang geodynamo simulations allow us to carry out less dissipative and, therefore, a more realistic dynamo regime study than ever before.  We have found that the thermal convection in the core is more turbulent, but the velocity field still keeps an organized structure with a set of columnar convection cells parallel to the rotation axis. In the Earth Simulator Center, the Yin-Yang grid is also applied to an advanced coupled simulation model of the global circulation of the atmosphere and ocean.  This presentation will:  (i) describe the basic ideas of the Yin-Yang grid and its implementation on the ES; and (ii) report on the current status of the application of this new capability to the geodynamo and mantle convection simulations.