Hybrid Delta Tracking Schemes Using a Track-Length Estimator

In Monte Carlo radiation transport calculations, Woodcock-delta tracking is a common alternative to the more popular surface tracking technique. In this work we introduce a delta-tracking algorithm that tallies fluxes to a structured rectilinear mesh using the track-length estimator. This development also enables hybrid surface-delta tracking algorithms, because the track-length tally can be used everywhere for scalar flux estimation regardless of which tracking algorithm is employed. We use this tallying technique to develop a novel hybrid-in-energy method. We also implement a hybrid-in-material method, like what is implemented in Serpent2. We demonstrate that these delta tracking algorithms can be used in conjunction with continuously moving surfaces. We compare these methods showing figures of merit on four time-dependent problems (multi-group and continuous energy) solved with CPU- and GPU-based computers. Our implementation of delta tracking with a track length tally modestly improves figures of merit compared to standard delta tracking with a collision estimator and surface tracking with a track length estimator (1.5X 2.5X) for a problem with significant void regions. For both multi-group and continuous energy pressurized water reactor benchmarks, standard delta tracking with a collision estimator performs best. Hybrid-in-energy methods show significant improvements (7X-11X) for a continuous energy reactor benchmark problem.