A multigroup method for radiation with scattering in three-dimensional hydrodynamic simulations

Substantial approximations in the treatment of radiation are still necessary in three-dimensional simulations in order to avoid extremely large computational costs. Solar radiation hydrodynamic simulations in three dimensions have previously assumed local thermodynamic equilibrium (LTE); an assumption that works well in the deep photosphere. This work aims at bringing these simulations a step further by including scattered radiation, with the goal of modeling chromospheres in three dimensions. We allow for coherent isotropic scattering, which alters the thermal structure and wave amplitudes in the chromosphere. Group mean opacity coefficients are used in group mean source functions that contain approximate scattering terms and exact contributions from thermal emissivity. The resulting three-dimensional scattering problem allows for a computationally efficient solution by a new iteration method. We have compared exact wavelength-integrated monochromatic solutions with the corresponding approximate solutions for solar conditions. We find that the total flux divergence obtained from the groups deviates less than 10% from the exact solution. When using these groups rather than the full monochromatic solution, the CPU time is reduced by a factor of about 100 in a test case for solar conditions.