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A Numerical Scheme for General Relativistic Magnetohydrodynamics

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C. F. Gammie, J. C. McKinney, G. Tóth
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Astrophysical Journal, 589, 444-457 (2003)
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We describe a conservative, shock-capturing scheme for evolving the
equations of general relativistic magnetohydrodynamics. The fluxes are
calculated using the Harten, Lax, & van Leer scheme. A variant of
constrained transport, proposed earlier by Tth, is used to maintain
a divergence-free magnetic field. Only the covariant form of the metric
in a coordinate basis is required to specify the geometry. We describe
code performance on a full suite of test problems in both special and
general relativity. On smooth flows we show that it converges at
second order. We conclude by showing some results from the evolution
of a magnetized torus near a rotating black hole.