  A numerical scheme is proposed for the solution of the three-dimensional
radiative transfer equation with variable optical depth. We show that
time-dependent ray tracing is an attractive choice for simulations of
astrophysical ionization fronts, particularly when one is interested in
covering a wide range of optical depths within a 3D clumpy medium. Our approach
combines the explicit advection of radiation variables with the implicit
solution of local rate equations given the radiation field at each point. Our
scheme is well suited to the solution of problems for which line transfer is
not important, and could, in principle, be extended to those situations also.
This scheme allows us to calculate the propagation of supersonic ionization
fronts into an inhomogeneous medium. The approach can be easily implemented on
a single workstation and also should be fully parallelizable.
