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We describe a 3D finite-difference spherical anelastic MHD (FSAM) code formodeling the subsonic dynamic processes in the solar convective envelope. Acomparison of this code with the widely used global spectral anlastic MHD code,ASH (Anelastic Spherical Harmonics), shows that FSAM produces convective flowswith statistical properties and mean flows similar to the ASH results. UsingFSAM, we first simulate the rotating solar convection in a partial sphericalshell domain and obtain a statistically steady, giant-cell convective flow witha solar-like differential rotation. We then insert buoyant toroidal flux tubesnear the bottom of the convecting envelope and simulate the rise of the fluxtubes in the presence of the giant cell convection. We find that for buoyantflux tubes with an initial field strength of 100 kG, the magnetic buoyancylargely determines the rise of the tubes although strong down flows producesignificant undulation and distortion to the shape of the emerging$\Omega$-shaped loops. The convective flows significantly reduce the rise timeit takes for the apex of the flux tube to reach the top. For the weakly twistedand untwisted cases we simulated, the apex portion is found to rise nearlyradially to the top in about a month, and produce an emerging region (at adepth of about 30 Mm below the photosphere) with an overall tilt angleconsistent with the active region tilts, although the emergence pattern is morecomplex compared to the case without convection. Near the top boundary at adepth of about 30 Mm, the emerging flux shows a retrograde zonal flow of about345 m/s relative to the mean flow at that latitude.

Three-Dimensional MHD Simulations of Emerging Active Region Flux in a  Turbulent Rotating Solar Convective Envelope: the Numerical Model and Initial  Results