Collision-based hybrid method
Time-dependent neutron transport is expensive because every time step needs a converged source iteration on fine energy and angular grids. Coarsening those grids makes each iteration cheaper, but it adds discretization error to the whole solution.
Approach
The collision-based hybrid method splits the transport equation into two equations at each time step. The uncollided equation contains the external and boundary sources and can be solved in a single iteration, so it is solved on fine energy and angular grids. The collided equation contains the scattering and fission terms, and the number of iterations it needs depends on the number of collisions, so it is solved on coarse grids. The two solutions are combined to give the flux for that time step.
My first paper on the method extended it to the multigroup setting. The second extended it to two spatial dimensions with a second-order time discretization, and improved how the energy groups are coarsened.
Results
In most of the time-dependent problems tested, the hybrid method is more efficient than the traditional multigroup approach. In two 2D problems it needed up to 50% less convergence time than an equivalent monolithic coarsening scheme, and it was more accurate in most of the low-fidelity comparisons.
Publications
- Collision-Based Hybrid Method for Two-Dimensional Neutron Transport Problems. Ben Whewell and Ryan G. McClarren, (2025). Nuclear Science and Engineering, 1-23. DOI: 10.1080/00295639.2025.2489778
- Multigroup Neutron Transport Using a Collision-Based Hybrid Method. Ben Whewell, Ryan G. McClarren, Cory D. Hauck, and Minwoo Shin, (2023). Nuclear Science and Engineering, 197:7, 1386-1405. DOI: 10.1080/00295639.2022.2154119
- Hybrid Numerical Methods and Solution Verification for the Neutron Transport Equation. Benjamin Joseph Whewell, (2024). University of Notre Dame. Dissertation. DOI: 10.7274/27927858.v1
Code
The method is implemented in ants (one and two dimensions) and discrete1 (one dimension).