An efficient short characteristic solution for the transfer equation in axisymmetric geometries using a spherical coordinate system

We present a new formulation of the short characteristic method for solving the transfer equation in axially symmetric systems. The radiation held is solved for on a grid in r and the spherical polar angle beta, with radiatio n coordinates chosen to take into account the spherical nature of the under lying source. Such a coordinate system is advantageous because it takes int o account the inherent discontinuities and symmetries due to the forward-pe aking nature of the radiation field. An important consequence of this is th at the determination of the boundary condition for the intensity along a sh ort characteristic does not involve an interpolation across a discontinuity . A parabolic approximation for the source function provides the best combi nation of accuracy, stability, and speed. Systematic errors introduced by u sing a weighted trapezoidal rule for quadrature in the radiation coordinate mu were overcome by using a monotonic cubic polynomial to approximate inte grands. The code has been successfully used to solve the polarized transfer equation and employs both an approximate operator iteration and Ng acceler ation to improve convergence. Comparison with an accurate long characterist ic code shows that a tremendous saving in computation time can be realized with a minimal loss of accuracy.