Hybrid block-AMR in cartesian and curvilinear coordinates: MHD applications

We present a novel, hybrid block-adaptive scheme for use in solving sets of near-conservation laws in general orthogonal coordinate systems. The adaptive mesh refinement (AMR) scheme is block-based, i.e. individual grids have a pre-fixed number of grid cells, and is implemented for any-dimensionality D. Its 'hybrid' character relaxes the common approach where a block that needs refinement triggers 2(D) subblocks when grids are refined by a factor of 2. This introduces 'incomplete families' in the grid hierarchy, but approaches the optimal fit to developing flow features inherent in the original patch-based AMR strategy. Our hybrid block-AMR approach is compared with a patch-based AMR one, both exploiting OpenMP parallelism. The implementation is able to handle general curvilinear coordinates, for which restriction and prolongation formulae are presented along with boundary treatments at 'singular' boundaries. Demonstrative examples cover hydro- and magnetohydrodynamic (MHD) applications, including tests on a 2D polar grid, a 2.5D spherical and a 3D cylindrical configuration. The applications cover classical up to relativistic MHD simulations, of particular relevance for astrophysical magnetized jet and stellar wind studies. (C) 2007 Elsevier Inc. All rights reserved.