Radiation hydrodynamics with many spectral lines: analytical expressions for a differentially moving slab. - Baschek, Bodo; Grueber, C.; Waldenfels, Wilhelm von; Wehrse, Rainer (Astronomy and astrophysics, 1997)
An analytical solution of the comoving frame radiative transfer equation for a differentially moving slab is obtained and written in terms of the wavelength-integrated extinction coefficient ψ, the spectral thickness. It is shown that ψ is much smoother than the extinction coefficient χ(λ) itself and that it can be well approximated e.g. by a simple piecewise linear function. Compared to conventional algorithms it allows speed-ups of factors >=10^5^ in the calculation of wavelength-integrated quantities such as e.g. the total flux, the radiative force, or the energy balance with an accuracy of <=1%. The total number of lines which can be taken into account is essentially unlimited. A simple expression for the total flux in the diffusion limit is derived and the dependencies on the velocity gradient are discussed.