Self-gravitational magnetohydrodynamics with adaptive mesh refinement for protostellar collapse

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 the divergence error of the magnetic field also implemented. The MHD solver exhibits a second-order accuracy in convergence tests of linearized MHD waves. The self-gravity is solved using a multigrid method composed of (1) a full multigrid (FMG)-cycle on the AMR hierarchical grids, (2) a V-cycle on these grids, and (3) an FMG-cycle on the base grid. The mulfigrid 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. Several tests are performed and the results indicate that the solutions are consistent with previously published results.