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

TL;DR

This paper introduces a collision-based hybrid method for 2D time-dependent neutron transport problems that improves convergence speed and accuracy by splitting equations and using different grid fidelities for collided and uncollided components.

Contribution

The paper presents a novel collision-based hybrid approach that enhances efficiency and precision in solving 2D multigroup neutron transport equations compared to traditional methods.

Findings

Faster convergence than monolithic coarsening schemes

Improved accuracy with high fidelity grids for uncollided solutions

Effective for multi-material, time-dependent problems

Abstract

A collision-based hybrid method for the discrete ordinates approximation of the multigroup neutron transport equation is developed for two-dimensional time-dependent problems. At each time step, this algorithm splits the neutron transport equation into two equations, where the external source is part of the uncollided equation and the fission and scattering sources are part of the collided equation. Low fidelity energy and angular grids are used with the collided transport solution to decrease convergence time while high fidelity grids are used with the uncollided transport solution to limit discretization error. The hybrid method is shown to be a better solution in terms of both convergence time and accuracy to traditional monolithic coarsening schemes. This advantage is demonstrated for two-dimensional time-dependent problems with different materials using a second order temporal discretization scheme.