A description is given of the algorithms implemented in the AstroBEARadaptive mesh refinement code for ideal magnetohydrodynamics. The code providesseveral high resolution, shock capturing schemes which are constructed tomaintain conserved quantities of the flow in a finite volume sense. Divergencefree magnetic field topologies are maintained to machine precision by collatingthe components of the magnetic field on a cell-interface staggered grid andutilizing the constrained transport approach for integrating the inductionequations. The maintenance of magnetic field topologies on adaptive grids isachieved using prolongation and restriction operators which preserve thedivergence and curl of the magnetic field across co-located grids of differentresolution. The robustness and correctness of the code is demonstrated bycomparing the numerical solution of various tests with analytical solutions orpreviously published numerical solutions obtained by other codes.
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