Collision-Based Hybrid Method for Two-Dimensional Neutron Transport Problems

A collision-based hybrid method for the discrete ordinates approximation of the multigroup neutron transport equation is developed for time-dependent problems. This expands upon previous multigroup work by extending the method to two spatial dimensions using a second-order temporal discretization scheme, and optimizes the energy group coarsening approach. For the collision-based hybrid method, the neutron transport equation is split into two equations at each time step. The first equation includes the uncollided terms of the neutron transport equation, the external and boundary sources, which can be solved in one iteration. The second equation is comprised of the collision terms, where the number of iterations is dependent on the number of collisions.

To minimize the required time for convergence, the collided equation uses low-fidelity energy and angular grids. To limit the discretization error from the coarser grid structures, the uncollided equation uses high-fidelity energy and angular grids. The solutions from the uncollided and collided transport equations are combined to estimate the flux at each time step.

This hybrid method is shown to be a better solution in terms of both convergence time and accuracy when compared to traditional monolithic coarsening schemes. In two time-dependent problems, the hybrid method is shown to use up to 50% less convergence time than an equivalent monolithic coarsening scheme. It is able to achieve this while remaining more accurate in most low-fidelity model comparisons.