  We present a new algorithm to solve the equations of radiation hydrodynamics
(RHD) in a frequency-integrated, two-moment formulation. Novel features of the
algorithm include i) the adoption of a non-local Variable Eddington Tensor
(VET) closure for the radiation moment equations, computed with a ray-tracing
method, ii) support for adaptive mesh refinement (AMR), iii) use of a
time-implicit Godunov method for the hyperbolic transport of radiation, and iv)
a fixed-point Picard iteration scheme to accurately handle the stiff nonlinear
gas-radiation energy exchange. Tests demonstrate that our scheme works
correctly, yields accurate rates of energy and momentum transfer between gas
and radiation, and obtains the correct radiation field distribution even in
situations where more commonly used -- but less accurate -- closure relations
like the Flux-limited Diffusion and Moment-1 approximations fail. Our scheme
presents an important step towards performing RHD simulations with increasing
spatial and directional accuracy, effectively improving their predictive
capabilities.
