Progress in the formulation of the approximate albedo boundary conditions for one-speed X,Y-geometry discrete ordinates and diffusion eigenvalue problems

We discuss in this paper the efficiency of approximate discrete ordinates (SN) and diffusion albedo boundary conditions for one-speed eigenvalue problems in X,Y geometry. The non-standard SN and diffusion albedos substitute approximately the baffle–reflector system around the active domain, as we neglect the transverse leakage terms within the two non-multiplying regions. Should the problem have no transverse leakage terms, i.e., one-dimensional slab geometry, then the offered albedo boundary conditions are exact. By efficiency we mean analyzing the accuracy of the numerical results versus the CPU execution time of each run for a given model problem. Numerical results to typical test problems are shown to illustrate this efficiency analysis.