Study of Flow in a Rotating and Precessing Spheroid Using an Overlapping-Grid Finite-Difference Code

A numerical code for solving the time-dependent incompressible dissipative MHD equations with finite differences on overlapping grids in a spheroid is being developed. It is based on a method developed by Henshaw (1994). 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. 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 Poincaré (1910) and Stewartson and Roberts (1963). Including the magnetic field, we are studying the dynamo action driven by the precession. We shall report the code structure, the boundary conditions, and the computational results in the studies mentioned above.