CS 267- Assignment 0: Numerical Geodynamo Simulations Erinna Chen Brief Bio I am a second year Planetary Science graduate student at UC Santa Cruz. My primary research interest is understanding the thermal evolution of icy satellites. Currently, I am using a parallelized magnetohydrodynamics code to model ocean dynamics driven by tidal deformation. My main motivation for taking this course is to gain experience in programming for parallel computers and to learn optimization techniques in the context of geophysical models. Simulating the Geodynamo The Earth’s magnetic field is generated by fluid motion within its liquid iron core. Three-dimensional simulations of convection-driven magnetohydrodnamic dynamos in rotating spherical shells are used to understand the origin of the magnetic field and to help explain the temporal and spatial variations in the field. The fluid flow in the core is very turbulent, and thus, the behavior of the magnetic field is unpredictable. Studies of the dynamo have looked at reproducing magnetic reversals and the effects of varying the boundary conditions. Figure 1: Three-dimensional magnetic field model during the transition in a magnetic field reversal. Several numerical codes have been developed to study the geodynamo (and the solar dynamo, in the astrophysical context). Each of these codes solves the three-dimensional equations for fluid motion with magnetic induction: continuity, conservation of momentum, conservation of energy, and the induction equation. In the angular coordinates, the velocity and magnetic fields are expanded in spherical harmonic coordinates. The non-linear terms in the equations are solved in grid space because of the computational efficiency, however this treatment requires transformation between spectral and grid space (spectral transform method). Codes vary by theirtreatment of the radial direction; some expand in Chebyshev polynomials, others using finite-difference methods. A code developed by Gary Glatzmaier to study the geodynamo is a model that employs Chebyshev polynomials in the radial direction. This code is written in Fortran and uses MPI for parallel communications. The code runs on various supercomputers, i.e. Columbia at NASA-Ames Research Center (No. 39). The bulk of time when running high resolution simulations is due to the all-to-all communications associated with the spectral transform method (O(n log n)). The code tends to use the vendor-provided Fast Fourier Transform (FFT) specific to the machine it is running on for performance reasons. Chebyshev polynomials also require global communication and data transfer. Finite-difference methods reduce this global communication; however, more grid points are required for solution convergence. References: Christensen, U.R. et al. 2001, A numerical dynamo benchmark, Phys. Earth Planet. Inter. 128, 25-34. Glatzmaier, G.A. and Roberts, P.H. 1997, Simulating the Geodynamo, Contemporary Phys. 38, 269-288. Roberts, P.H. and Glatzmaier, G.A. 2000, Geodynamo theory and simulations, Rev. Mod. Phys. 72,
View Full Document
Unlocking...