Theory and analysis of accuracy for the method of characteristics direction probabilities with boundary averaging

The method of characteristic direction probabilities (CDP) combines the benefits of the collision probability method (CPM) and the method of characteristics (MOC) for the solution of the integral form of the Botlzmann Transport Equation. By coupling only the fine regions traversed by the characteristic rays in a particular direction, the computational effort required to calculate the probability matrices and to solve the matrix system is considerably reduced compared to the CPM. Furthermore, boundary averaging is performed to reduce the storage and computation but the capability of dealing with complicated geometries is preserved since the same ray tracing information is used as in MOC. An analysis model for the outgoing angular flux is used to analyze a variety of outgoing angular flux averaging methods for the boundary and to justify the choice of optimize averaging strategy. The boundary average CDP method was then implemented in the Michigan PArallel Characteristic based Transport (MPACT) code to perform 2-D and 3-D transport calculations. The numerical results are given for different cases to show the effect of averaging on the outgoing angular flux, region scalar flux and the eigenvalue. Comparison of the results with the case with no averaging demonstrates that an angular dependent averaging strategy is possible for the CDP to improve its computational performance without compromising the achievable accuracy.