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A new code and methodology are introduced for solving the generalrelativistic magnetohydrodynamic (GRMHD) equations in fixed backgroundspacetimes using time-explicit, finite-volume discretization. The code hasoptions for solving the GRMHD equations using traditional artificial-viscosity(AV) or non-oscillatory central difference (NOCD) methods, or a new extended AV(eAV) scheme using artificial-viscosity together with a dualenergy-flux-conserving formulation. The dual energy approach allows foraccurate modeling of highly relativistic flows at boost factors well beyondwhat has been achieved to date by standard artificial viscosity methods. Itprovides the benefit of Godunov methods in capturing high Lorentz boosted flowsbut without complicated Riemann solvers, and the advantages of traditionalartificial viscosity methods in their speed and flexibility. Additionally, theGRMHD equations are solved on an unstructured grid that supports local adaptivemesh refinement using a fully threaded oct-tree (in three dimensions) networkto traverse the grid hierarchy across levels and immediate neighbors. A numberof tests are presented to demonstrate robustness of the numerical algorithmsand adaptive mesh framework over a wide spectrum of problems, boosts, andastrophysical applications, including relativistic shock tubes, shockcollisions, magnetosonic shocks, Alfven wave propagation, blast waves,magnetized Bondi flow, and the magneto-rotational instability in Kerr blackhole spacetimes.Comment: 41 pages, 16 figs, to appear in The Astrophysical Journa

Cosmos++: Relativistic Magnetohydrodynamics on Unstructured Grids with Local Adaptive Refinement