Benchmark-Quality Results for Transport Problems Involving a Void Region in Spherical Geometry

The post-processed spherical harmonics () method is used to solve four monoenergetic test problems in spherical geometry that include a void region in their definition. Two of them are two-region problems and the remaining ones are three-region problems. It is shown how the void region can be excluded from the problem and how a solution can be obtained for it once the reduced problem is solved. Numerical results with six significant digits of accuracy for the scalar flux, the current, and the angular flux are provided for all of the problems. A comparison with tabulated scalar flux results obtained by other authors for one of the problems is carried out and serves to illustrate the convergence difficulties of transport methods based on spatial discretization when used in voids.