HR: 0800h
AN: GP31A-0080    [Abstracts]
TI: A Numerical Method for Geodynamo Simulations Based on Fourier Expansion and Finite Difference: Comparison With Spectral Transform Method
AU: * Oishi, Y
EM: yoishi@eps.s.u-tokyo.ac.jp
AF: Department of Earth and Planetary Physics, University of Tokyo , 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033 Japan
AU: Sakuraba, A
EM: sakuraba@eps.s.u-tokyo.ac.jp
AF: Department of Earth and Planetary Physics, University of Tokyo , 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033 Japan
AU: Hamano, Y
EM: hamano@eps.s.u-tokyo.ac.jp
AF: Department of Earth and Planetary Physics, University of Tokyo , 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033 Japan
AB: In simulating three-dimensional thermal convection and a dynamo process in a rotating and electrically conducting fluid spherical shell, the most general method is a spectral transform method (STM) in which variables are expanded by spherical harmonics but transformations between spectral and grid spaces are required at each timestep to calculate the non-linear terms. This method is suitable for geodynamo simulations because it has good accuracy and also enables appropriate treatment of boundary conditions of a magnetic field. However, the calculation amount of the Legendre transformation is proportional to N⁴, N being a number of degrees of freedom per one dimension. This calculation amount causes a heavy drag especially on the large-N calculation which is necessary for simulations at Earth-like parameters. We therefore developed a new method for geodynamo simulations which needs fewer calculations. This method avoids the time-consuming Legendre transformation and performs only the Fourier transformation in longitude. The resulting spectral equations are solved in a meridional plane by using a finite difference technique. The amount of calculations of this method is proportional to N³ log N, so the margin between this method and STM becomes wide when N is large. For the verification of this method we solved Case 0 (rotating non-magnetic convection) and Case 1 (self-exciting dynamo with an insulating inner core) of the dynamo benchmark problems (Christensen et al., 2001) whose solutions are stationary aside from an azimuthal drift. In the benchmark some values which indicate the properties of the solutions were defined for the quantitative comparisons. All of these values of Case 0 and Case 1 except for the angular frequency of the azimuthal drift of Case 0 were in agreement to the standard solutions of the benchmark within about 0.5 %. The error level of the drift frequency of Case 0 was about 8 %. We also performed some dynamo simulations with higher Rayleigh and lower Ekman numbers than those of the benchmark, and compared the solutions to those of STM. This comparison also showed an acceptable consistency. In addition to these verifications, the calculation performance of the present method on a massively parallel supercomputer will also be shown in this presentation and the effectivity of this method will be discussed.
DE: 1510 Dynamo: theories and simulations
SC: Geomagnetism and Paleomagnetism [GP]
MN: Fall Meeting 2005