HR: 0800h
AN: GP11D-0847    [Abstracts]
TI: Study of Nearly Inviscid Flow in a Rotating and Precessing Spheroid
AU: * Wu, C
EM: ccwu@ucla.edu
AF: Institute of Geophysics and Planetary Physics, University of California, 405 Hilgard Ave, Los Angeles, CA 90095 United States
AU: Roberts, P H
EM: roberts@math.ucla.edu
AF: Institute of Geophysics and Planetary Physics, University of California, 405 Hilgard Ave, Los Angeles, CA 90095 United States
AB: A numerical code for solving the time-dependent incompressible MHD equations with finite differences on overlapping grids in a spheroid is being developed. In our code, the momentum equation for the velocity and the induction equation for the magnetic field are solved together with the Poisson equation for the pressure. The velocity and the magnetic field are advanced explicitly in time using a Runge-Kutta scheme. The grids are chosen to overcome pole and origin problems, which limit the time-step size, and to enhance spatial resolution at places where high resolution is required such as at boundary layers. A new approach is used in evaluating the numerical fluxes for both the momentum and the induction equations. The method is based on modern shock capturing schemes for compressible fluids, such as ENO (Essentially Non-Oscillatory), WENO (Weighted-ENO), and Central schemes. The key idea of these schemes is to approximate the fluxes to high order and to avoid the creation of spurious oscillations in the solution. The new incompressible code conserves both momentum and the magnetic fluxes. It is found to be numerically stable without the need for explicit dissipation terms. This is significant when seeking flows in systems such as the Earth's core where the Ekman number and magnetic Prandtl number are very small. We are using this code to study the fluid motion in a rotating and precessing spheroid, a significant problem in astrophysics and geophysics. In the non-magnetic case, the numerical solutions for both viscous and pressure couplings are consistent with those of Poincar\'e (1910) and Stewartson and Roberts (1963). Including the magnetic field, we investigate dynamo action driven by the precession. We shall report the numerical method, the boundary conditions, and the computational results in the studies mentioned above.
DE: 3200 MATHEMATICAL GEOPHYSICS (New field)
DE: 3230 Numerical solutions
DE: 1500 GEOMAGNETISM AND PALEOMAGNETISM
DE: 1510 Dynamo theories
SC: Geomagnetism and Paleomagnetism [GP]
MN: 2004 AGU Fall Meeting