| Title: | Pseudospectral Methods Applied to Computational Magnetohydrodynamics - Application to Earth's Deep Interior |
| Date: |
January 8, 2007 (Monday)
|
| Time: |
2:30 p.m. - 3:30 p.m.
|
| Venue: |
Room 121, 1/F, Ho Sin-hang Engineering Building,
The Chinese University of Hong Kong, Shatin, N.T. |
| Speaker: |
Dr. Steven J. Pearce
School of Computing Science Simon Fraser University Canada |
Many physical systems found on astrophysical scales and in the laboratory, involving superconducting fluids, are describable by a coupled set of partial differential equations describing the nonlinear interaction between an electrically conducting fluid and an embedded magnetic field. This field of study is collectively known as magnetohydrodynamics. Such mathematical models are only solvable numerically at present. Moreover, the highly nonlinear nature of the system equations requires extremely accurate approximation techniques - the finite element method is often inadequate. Recent advances in spectral methods and, in particular, applying a form of collocation has remedied this situation allowing for significant progress in research. The first part of this talk is a review of the spectral collocation technique.
A specific application of this advanced numerical methodology is reviewed next; namely, the effect of sudden changes in the Earth's moment of inertia upon the hydromagnetic state of its core. In particular, variations in georotation, in response to ice age transgressions and regressions, are described as varying boundary conditions in an axisymmetric Earth model containing both viscous and electromagnetic coupling. The deterministic (inertia-free) equations, describing the limit of rapid rotation, are explored. A fully de-aliased pseudo-spectral technique is utilized for solving the incompressible magneto-fluid equations. The variables are collocated in radius using Chebyshev polynomials whereas the colatitudinal variables are evaluated pseudo-spectrally using associated Legendre polynomials. Time dependence and magnetic diffusion are controlled by a modified second order semi-implicit Runge-Kutta scheme. Steady state boundary layers, arising from differential motion of the outer core boundaries, were found to induce significant geomagnetic transients. Within the context of this model, it is concluded that a causal connection is plausible between geomagnetic transients and significant changes in the Earth's moment of inertia.
BIOGRAPHY:
Dr. Steven Pearce received a B. Sc degree and a M. Sc. degree in Geophysics from University of British Columbia and a Ph.D. degree in Astrophysics and Applied Mathematics from University of Arizona.
He is a faculty member of the School of Computing Science at Simon Fraser University and currently on faculty exchange with Zhejiang University.
Enquiries: Miss Temmy So at tel 2609 8444
For more information, please refer to http://www.cse.cuhk.edu.hk/seminar