Numerical Simulations of Stellar Convective Dynamos. I. The Model and Method*

A numerical model used to simulate global convection and magnetic field generation in stars is described. Nonlmear, three-dimensional, time-dependent solutions of the anelastic magnetohydrodynamic equations are presented for a stratified, rotating, spherical, fluid shell heated from below. The velocity, magnetic field, and thermodynamic perturbations are expanded in spherical harmonics to resolve their horizontal structure and in Chebyshev polynomials to resolve their radial structure. An explicit Adams-Bashforth time integration scheme is used with an implicit Crank-Nicolson treatment of the diffusion terms. Nonlinear terms are computed in physical space; and spatial derivatives are computed in spectral space. The resulting second-order differential equations are solved with a Chebyshev collocation method. Preliminary solutions for a Solar-like model are briefly discussed. Convective motions driven in the upper, superadiabatic part of the zone penetrate into the lower, subadiabatic part of the zone. Differential rotation, induced by the interaction of convection and rotation, is an equatorial acceleration at the surface as observed on the Sun; below the surface angular velocity decreases with depth. The meridional circulation and the equator-pole temperature excess are within Solar observational constraints; however, the giant-cell velocities at the surface are larger than observed. The large-scale magnetic field, induced by the differential rotation and helical motions, peaks in the subadiabatic region below the convection zone; and, near the top of the convection zone, it is concentrated over the downdrafts of giant cells. A systematic drift in latitude of the magnetic field or a field reversal has not yet been seen.