  In order to constrain the models describing circumstellar environments, it is
necessary to solve the radiative transfer equation in the presence of
absorption and scattering, coupled with the equation for radiative equilibrium.
However, solving this problem requires much CPU time, which makes the use of
automatic minimisation procedures to characterise these environments
challenging. The use of approximate methods is then of primary interest. One
promising candidate method is the flux-limited diffusion (FLD), which recasts
the radiative transfer problem into a non-linear diffusion equation. One
important aspect for the accuracy of the method lies in the implementation of
appropriate boundary conditions (BCs). We present new BCs for the FLD
approximation in circumstellar environments that we apply here to spherically
symmetric envelopes. At the inner boundary, the entering flux (coming from the
star and from the envelope itself) may be written in the FLD formalism and
provides us with an adequate BC. At the free outer boundary, we used the FLD
formalism to constrain the ratio of the mean radiation intensity over the
emerging flux. In both cases we derived non-linear mixed BCs relating the
surface values of the mean specific intensity and its gradient. We implemented
these conditions and compared the results with previous benchmarks and the
results of a Monte Carlo radiative transfer code. A comparison with results
derived from BCs that were previously proposed in other contexts is presented
as well. For all the tested cases, the average relative difference with the
benchmark results is below 2\% for the temperature profile and below 6\% for
the corresponding spectral energy distribution or the emerging flux. We point
out that the FLD method together with the new outer BC also allows us to derive
an approximation for the emerging flux.
