Impact of ray generation schemes on the random ray method for eigenvalue and shielding applications

Abstract

As a variant of the Method Of characteristics (MOC), The Random Ray Method (TRRM) stochastically generates the characteristic rays within the solution domain, making it a stochastic-deterministic hybrid method for the particle transport calculation. Compared to traditional MOC, TRRM significantly reduces computational memory footprint and greatly enhances the flexibility of MOC for a high-fidelity 3D simulation of reactors. However, the introduction of stochastic discretization leads to uncertainty with a convergence rate of $O\left(N^{-1/2}\right)$ in the results of TRRM, akin to the standard Monte Carlo method. This study focuses on improving the performance of TRRM by investigating different ray generation schemes, which are divided into two components: sampling methods and random number generation techniques. Three sampling strategies—uniform sampling, mesh-based stratified sampling, and Latin hypercube sampling—are combined with two random number generation techniques—pseudo-random numbers (PRN) and Low-Discrepancy Sequences (LDS)—to create six distinct schemes. The performance of these schemes is evaluated using the 2D C5G7 criticality benchmark and the 3D Kobayashi fixed-source benchmark. Numerical results from the C5G7 benchmark show that the combination of uniform sampling and LDS yields the best performance, reducing the uncertainty in k_eff and decreasing the required calculation time for active batches by more than a factor of seven. Latin hypercube sampling also demonstrates better performance, but its combination with LDS yields no benefits. For the Kobayashi benchmark, the uniform sampling with LDS also shows best performance, but advanced sampling methods like stratified and Latin hypercube sampling do not offer significant improvements and can introduce statistical oscillations. Therefore, the uniform sampling with LDS is highly recommended for TRRM on further applications.