Parallel solutions of the neutron transport equation in two- and three-dimensions by the collision probability method

This work addresses the limitations found in modern reactor analysis codes by using a combination of parallel processing and geometrical domain decomposition. The collision probability (CP) method was extended from the commonly used two-dimensional (2D) to a full three- dimensional (3D) set of coupled equations. Using the GTRAN2 computer program by Dr. Jasmina L. Vujic as a reference point, the 3D CP theory as well as various approximation and numerical acceleration techniques were derived and implemented to create the new computer program, MAGGENTA. In both 2D and 3D version of MAGGENTA, the employed collision probability methodology preserves fine spatial and energy detail for the entire region of interest. MAGGENTA also benefits from the additional computing power gained by using parallel supercomputers or networks of workstations communicating via the Message Passing Interface (MPI) standard. The parallel algorithms developed in this work are based on the decomposition of large spatial domains into subdomains, which are coupled through angularly dependent interface currents. The directionally-dependent collision/transfer probabilities are defined and calculated. This unique implementation of the CP method, current coupling, neutron rebalance, and parallel programming techniques has achieved accuracy and efficiency not found elsewhere in current literature. In 2D, large multi-assembly problems were successfully performed with MAGGENTA while preserving the fine spatial detail on each assembly. A problem consisting of 64 fuel assemblies, with 996 flat flux zones on each assembly, and 20 energy groups was solved in less than 50 minutes on 64 SP2 processors. A 3D solution of a full BWR fuel assembly was performed and compared with results from the Monte Carlo code MCNP. Using up to 112 processors, this problem was solved in 1.5 hours with an average pin cell flux error of less than one percent from the MCNP solution. While the 2D version of MAGGENTA has already been used for analysis of advanced reactor designs, the 3D version shows great promise. Following additional studies and optimization of the 3D matrix generation, MAGGENTA can become an excellent tool for providing the detailed transport calculations needed in advanced reactor safety, fuel performance, and even medical radiation treatment calculations.