New boundary conditions for the approximate flux-limited diffusion radiative transfer in circumstellar environments. Test case study for spherically symmetric envelopes

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