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

Substantial approximations in the treatment of radiation are still necessar y in three-dimensional simulations in order to avoid extremely large comput ational costs. Solar radiation hydrodynamic simulations in three dimensions have previously assumed local thermodynamic equilibrium (LTE); an assumpti on that works well in the deep photosphere. This work aims at bringing thes e simulations a step further by including scattered radiation, with the goa l of modeling chromospheres in three dimensions. We allow for coherent isot ropic scattering, which alters the thermal structure and wave amplitudes in the chromosphere. Group mean opacity coefficients are used in group mean s ource functions that contain approximate scattering terms and exact contrib utions 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 solution s with the corresponding approximate solutions for solar conditions. We fin d that the total flux divergence obtained from the groups deviates less tha n 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 i n a test case for solar conditions.