A new numerical code, called SFUMATO, for solving self-gravitational
magnetohydrodynamics (MHD) problems using adaptive mesh refinement (AMR) is
presented. A block-structured grid is adopted as the grid of the AMR hierarchy.
The total variation diminishing (TVD) cell-centered scheme is adopted as the
MHD solver, with hyperbolic cleaning of divergence error of the magnetic field
also implemented. The self-gravity is solved by a multigrid method composed of
(1) full multigrid (FMG)-cycle on the AMR hierarchical grids, (2) V-cycle on
these grids, and (3) FMG-cycle on the base grid. The multigrid method exhibits
spatial second-order accuracy, fast convergence, and scalability. The numerical
fluxes are conserved by using a refluxing procedure in both the MHD solver and
the multigrid method. The several tests are performed indicating that the
solutions are consistent with previously published results.Comment: 23 pages, 15 figures. PASJ in press. Document with high resolution
figures is available in
http://redmagic.i.hosei.ac.jp/~matsu/AMR06/matsumotoAMR.pd
