Bidirectional reflective boundary conditions and the analytical smoothing technique for the spherical harmonics method of radiative transfer

Abstract Two techniques are presented to improve the generality of the spherical harmonics solution. We first exploit the properties of the matrices encountered in the spherical harmonics method and develop a technique that handles bidirectionally reflective boundary conditions. To damp the undesirable oscillatory phenomenon in the spherical harmonics solution, an integral smoothing is usually applied. For the second technique, we present an analytical smoothing which requires little computation overhead and preserves the nice features of an analytical solution.