Unconditionally Stable Diffusion-Synthetic Acceleration Methods for the Slab Geometry Discrete Ordinates Equations. Part I: Theory

We consider the slab geometry discrete ordinates equations, with the weighted diamond, linear characteristic, linear discontinuous, and linear moments spatial differencing schemes. For each differencing scheme we derive a diffusion-synthetic, source-correction acceleration method which, for model (infinite medium, isotropic scattering, constant cross section, constant mesh spacing) problems, unconditionally reduces the spectral radius of the iteration method from the unaccelerated value of c (the scattering ratio) to <c/3.