  We propose an explicit-implicit scheme for numerically solving Special
Relativistic Radiation Hydrodynamic (RRHD) equations, which ensures a
conservation of total energy and momentum (matter and radiation). In our
scheme, 0th and 1st moment equations of the radiation transfer equation are
numerically solved without employing a flux-limited diffusion (FLD)
approximation. For an hyperbolic term, of which the time scale is the light
crossing time when the flow velocity is comparable to the speed of light, is
explicitly solved using an approximate Riemann solver. Source terms describing
an exchange of energy and momentum between the matter and the radiation via the
gas-radiation interaction are implicitly integrated using an iteration method.
The implicit scheme allows us to relax the Courant-Friedrichs-Lewy condition in
optically thick media, where heating/cooling and scattering timescales could be
much shorter than the dynamical timescale. We show that our numerical code can
pass test problems of one- and two-dimensional radiation energy transport, and
one-dimensional radiation hydrodynamics. Our newly developed scheme could be
useful for a number of relativistic astrophysical problems. We also discuss how
to extend our explicit-implicit scheme to the relativistic radiation
magnetohydrodynamics.
