A COMPARISON OF STOCHASTIC MESH CELL VOLUME COMPUTATION STRATEGIES FOR THE RANDOM RAY METHOD OF NEUTRAL PARTICLE TRANSPORT

Argonne National Laboratory 9700 S. Cass Avenue Lemont, IL, USA

{jtramm,siegela,alund,promano}@anl.gov

Published online: 22 February 2021

Abstract

The random ray method is a recently developed neutron transport method that can be used to perform efficient full-core, general-purpose, high-fidelity 3D simulations of nuclear reactors. While Tramm et al. have so far documented the new random ray algorithm in several publications, one critical detail has not yet been published: how to best determine the volume of each source region (or cell) of the simulation. As the “true” analytical constructive solid geometry cell volumes are typically not known a priori they must be computed by the application at runtime, which is not straightforward in TRRM as different rays are used each power iteration such that the sampled volume of each cell also changes between iterations. In the present study, we analyze two different on-the-fly stochastic methods for computing the cell volumes and quantify their impacts on the accuracy of scalar flux estimates. We find that the “na¨ıve” stochastic volume estimator (which arises naturally from the derivation of the Method of Characteristics), is highly biased and can result in over 1,000 pcm error in eigenvalue. Conversely, we find that the “simulation averaged” estimator is unbiased and is therefore equivalent to the use of analytical cell volumes even when using a coarse ray density. Thus, the new simulation averaged method is a critical (and as yet undocumented) component of the TRRM algorithm, and is therefore vital information for those in the reactor physics community working to implement random ray solvers of their own.