Radiative transfer in 3D numerical simulations

We simulate convection near the solar surface, where the continuum optical depth is of order unity. Hence, to determine the radiative heating and cooling in the energy conservation equation, we must solve the radiative transfer equation (instead of using the diffusion or optically thin cooling approximations). A method efficient enough to calculate the radiation for thousands of time steps is needed. We assume LTE and a non-gray opacity grouped into 4 bins according to strength. We perform a formal solution of the Feautrier equation along a vertical and four straight, slanted, rays (at four azimuthal angles which are rotated 15 deg. every time step). We present details of our method. We also give some results: comparing simulated and observed line profiles for the Sun, showing the importance of 3D transfer for the structure of the mean atmosphere and the eigenfrequencies of p-modes, illustrating Stokes profiles for micropores, and analyzing the effect of radiation on p-mode asymmetries.