HR: 0800h
AN: T11E-1330    [Abstracts]
TI: Application of the Yin-Yang grid to three-dimensional spherical shell convection at infinite Prandtl number
AU: * Yoshida, M
EM: myoshida@jamstec.go.jp
AF: Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology, 3173-25 Showa-machi, Kanazawa-ku, Yokohama, 236-0001 Japan
AU: Kageyama, A
EM: kage@jamstec.go.jp
AF: Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology, 3173-25 Showa-machi, Kanazawa-ku, Yokohama, 236-0001 Japan
AB: We have developed a new numerical simulation code to solve the thermal convection of a Boussinesq-approximation fluid with infinite Prandtl number and spatially variable viscosity using ``Yin-Yang'' grid [Yoshida and Kageyama, 2004]. The Yin-Yang grid, which has been recently proposed by Kageyama and Sato [2004], is composed of two component grids that have exactly the same shape and size. A component grid of the Yin-Yang grid is actually a low-latitude part of the latitude-longitude grid on spherical polar coordinates. The Yin-Yang grid is suitable to solve the mantle convection problems because it automatically avoids the pole problems, i.e., both the coordinate singularity and grid convergence, that are inevitable in the latitude-longitude grid. The non-dimensional equations of mass, momentum and energy conservation governing the thermal convection are solved by the finite difference discretization with second-order accuracy. Using the Yin-Yang grid, we simultaneously solve these equations for each component grid (i.e., ``Yin grid'' and ``Yang grid''). We use the collocated grid method; all the primitive variables, velocity, pressure, and temperature, are defined on the same grid points. The SIMPLER method is applied to solve velocity and pressure. The Crank-Nicolson method is used in the energy equation for the time stepping. The horizontal boundary values of each component grid are determined by linear interpolation of another component grid. We performed benchmark tests with published numerical codes [e.g., Richards et al., 2001] and confirmed the validity of our code. When $Ra = 10^5$, the convection patterns become weakly time-dependent; the geometrical ``cubic'' symmetry at $Ra = 10^4$ is broken. The corresponding case in which a finite volume scheme on the latitude-longitude grid is used shows a symmetric pattern about equator and appears to remain in a steady state. These observations suggest that convections are numerically affected by pole problems in the latitude-longitude grid. On the other hand, the pole problems are removed in our code by making use of Yin-Yang grid.
DE: 8120 Dynamics of lithosphere and mantle--general
DE: 8121 Dynamics, convection currents and mantle plumes
SC: Tectonophysics [T]
MN: 2004 AGU Fall Meeting