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We describe a conservative, shock-capturing scheme for evolving the equationsof general relativistic magnetohydrodynamics. The fluxes are calculated usingthe Harten, Lax, and van Leer scheme. A variant of constrained transport,proposed earlier by T\'oth, is used to maintain a divergence free magneticfield. Only the covariant form of the metric in a coordinate basis is requiredto specify the geometry. We describe code performance on a full suite of testproblems in both special and general relativity. On smooth flows we show thatit converges at second order. We conclude by showing some results from theevolution of a magnetized torus near a rotating black hole.Comment: 38 pages, 18 figures, submitted to Ap

HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics