A first collision method for discrete ordinates k-eigenvalue problems

Ray effects are an inherent drawback of the discrete ordinates method. In criticality problems, ray effects can cause the multiplication factor or k-eigenvalue to vary dramatically with the numbers of discretized angles. One method of mitigating ray effects is the first collision method whereby the flux is split into collided and uncollided components and the once collided flux is found from the uncollided flux and used as a source in the collided flux solution. The first collision method is implemented in discrete ordinates codes for a one-dimensional sphere and the LANL production code PARTISN. The implementation of the codes are verified by comparison of the solutions to analytical benchmark solutions. The effectiveness of the first collision method is tested through two array problems: a 2 x 2 array of 4.5cm square sources and a 5 x 5 array of 4.5cm sources surrounded by vacuum. These test problems show oscillation in the k-eigenvalue. It is shown that with ray tracing a low precision answer can be found with a reliable error band at the cost of a large increase in computational time.; The ray tracing method of finding the first collision source introduces a stochastic error into the uncollided flux and first collision source. The results show that the variation in total fission source must be less than the tolerance setting for the algorithm to converge reliably.; Finally a parallel profiling of efficiency and speed up is performed for the first collision methods and compared to the conventional discrete ordinates method. The main conclusions drawn here is the conventional discrete ordinates method and first collision by discrete ordinates method scale similarly and the scaling is dependent upon the size of the problem.; In the end, the first collision method is not a final solution for ray effects in discrete ordinates eigenvalue problems, but for some problems it can provide a tool to obtain a reliable solution more quickly than the conventional discrete ordinates method.