  An approximate Riemann solver for the equations of relativistic
magnetohydrodynamics (RMHD) is derived. The HLLC solver, originally developed
by Toro, Spruce and Spears, generalizes the algorithm described in a previous
paper (Mignone & Bodo 2004) to the case where magnetic fields are present. The
solution to the Riemann problem is approximated by two constant states bounded
by two fast shocks and separated by a tangential wave. The scheme is
Jacobian-free, in the sense that it avoids the expensive characteristic
decomposition of the RMHD equations and it improves over the HLL scheme by
restoring the missing contact wave.
  Multidimensional integration proceeds via the single step, corner transport
upwind (CTU) method of Colella, combined with the contrained tranport (CT)
algorithm to preserve divergence-free magnetic fields. The resulting numerical
scheme is simple to implement, efficient and suitable for a general equation of
state. The robustness of the new algorithm is validated against one and two
dimensional numerical test problems.
