Variance Reduction and Optimization Strategies in a Biased Woodcock Particle Tracking Framework

A novel particle tracking framework is introduced in this paper that utilizes null-collisions to sample distance to collision in Monte Carlo particle transport problems. The sampling process is described in the most general form as it covers all of the main developments concerning the Woodcock method (delta tracking). We show that none of the previously suggested modifications are optimal in terms of either variance or efficiency. Variance analysis is provided for a general transport problem along with the estimation of computational cost. Simplified models with analytic solutions are further investigated and propositions for optimal settings are discussed based on the derived equations. A well-known variance reduction technique, exponential transform, is found to be a limiting case of the biased Woodcock tracking method and comparison shows the proposed framework may outperform the exponential transform in real-case scenarios.