Comparison of the Order of Approximation in Several Spatial Difference Schemes for the Discrete-Ordinates Transport Equation in One-Dimensional Plane Geometry

A systematic comparison has been made of the local difference operator approximation in spatial difference schemes for the solution of the transport equation in slab geometry by the method of discrete ordinates. The truncation error in different schemes varies according to the nature of the intra-mesh source and flux interpolation, and this explains the good performance of certain recently proposed schemes. We have classified the schemes according to the nature of the intra-mesh source interpolation. As a general principle, we find that in each class, the scheme that conserves the spatial moments of source calculated from the previous iteration and avoids flux interpolation is the most accurate.