Geodynamo Simulations Using a High Order Cartesian Magnetohydrodynamics Code

Details Geodynamo Simulations Using a High Order Cartesian Magnetohydrodynamics Code Geodynamo Simulations Using a High Order Cartesian Magnetohydrodynamics Code

Dec 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003agufmgp11c0280m&link_type=abstract

American Geophysical Union, Fall Meeting 2003, abstract #GP11C-0280

Statistics

Computation

1507 Core Processes (8115), 1510 Dynamo Theories, 5440 Magnetic Fields And Magnetism, 5734 Magnetic Fields And Magnetism, 7524 Magnetic Fields

Scientific paper

Most numerical simulations of the geodynamo are cast in spherical geometry, using a spherical harmonic representation for lateral variations and an expansion in Chebyshev polynomials or discretisation in radius. A number of research groups have produced time dependent, three dimensional, self-consistent solutions to the geodynamo problem using this pseudospectral methodology. Computational limitations currently place a practical bound on the parameter regime that can be explored in this context, with values appropriate for Earth out of reach by several orders of magnitude. For the spherically pseudospectral codes, the absence of an efficient Legendre transform is a strong factor contributing to this limitation. As a first step towards alternative computational methods for geodynamo modelling, we have adapted an existing, efficiently parallelised magnetohydrodynamics (MHD) code, originally developed for weakly compressible, turbulent astrophysical MHD problems. The Pencil-Code (Dobler and Brandenburg, reference URL) is a Cartesian code that uses sixth-order finite differences, applied to ``pencils'' (i.e. array sections) in the x direction in a cache-efficient way. The domain is tiled in the y and z directions, with the communication of boundary elements handled by Message Passing Interface (MPI). Time stepping is via a third order Runge-Kutta method. The code's modular structure allows a flexible selection of various physical processes and variables, making it easily adaptable for many types of MHD problems, including the geodynamo. Modifications toward a viable planetary dynamo code include the implementation of the spherical shell geometry of Earth's outer core, and modifications of the hydrodynamic and thermodynamic modules towards the Boussinesq or anelastic approximations. We report on our current feasibility study and compare preliminary results with physically similar spherical computations and the geodynamo benchmark (Christensen et al., Phys. Earth Planet. Int., 128, 25-34, 2001).

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