HR: 0800h
AN: GP31A-0083    [Abstracts]
TI: Sub-grid scale model for dynamo simulations in a rotating plane layer model --- Dealing with unstructured grids
AU: * Matsui, H
EM: matsui@geosci.uchicago.edu
AF: Dept. of Geophysical Sciences, the University of Chicago, 5734 S Ellis Ave., Chicago, IL 60637 United States
AU: Buffett, B A
EM: buffett@geosci.uchicago.edu
AF: Dept. of Geophysical Sciences, the University of Chicago, 5734 S Ellis Ave., Chicago, IL 60637 United States
AB: The Sub-grid scale modeling is required for the geodynamo simulations because the fluid motion and the magnetic field in the Earth's outer core have small scale components which cannot be resolved in numerical simulations. We model the influence of sub-grid scale motion for the momentum and heat flux, the Lorentz force, and the induction term using the nonlinear gradient model by Leonard (1974), which is a form of the scale similarity model. The result suggests that the nonlinear gradient model can represent basic characteristics of the effects of the sub-grid scale motion, but we observe some discrepancies which are due to the spatial dependence of the filter function when the grid is non-equidistant. Ghosal and Moin (1995) point out that this error arises when the order of filtering and spatial differentiation operation is changed. In the present study, we correct the commutation error specifically for the nonlinear gradient model. In this case, the commutation error can be written as the product of derivative of the second order moment of the filter function and second derivative of the field. We append this correction term to our model, and evaluate the SGS terms from a snapshot of a MHD simulation in a rotating plane layer model. The prediction shows that the correction of the commutation error substantially improves the predicted SGS terms around the boundaries when compared with a direct estimate of SGS terms on the finer grid. In fact, the magnitude of the correction for the divergence of SGS terms is comparable to the uncorrected prediction of the nonlinear gradient model. These results indicate that the addition of the present correction for the spatial derivative is necessary to obtain the correct SGS terms for unstructured grid, such as the plane layer model or spherical shell model.
DE: 0545 Modeling (4255)
DE: 1510 Dynamo: theories and simulations
SC: Geomagnetism and Paleomagnetism [GP]
MN: Fall Meeting 2005