Ray effects mitigation using the Monte Carlo first collision source method and application to the Kobayashi benchmark problems

The problem of ray effects, arising in the calculation of local source problems with low scattering media, have been perplexing the discrete ordinates (S_N) method. Conventionally, the first collision source technique based on deterministic methods is used to remedy ray effects. In this paper, we investigate a technique based on Monte Carlo method to calculate first collision source distributions and consequently mitigate the ray effects. The Monte Carlo first collision source (MC-FCS) method has been implemented into the three-dimensional (3D) parallel S_N transport code Marvin. The 3D Kobayashi benchmark problems were used to systematically verify effectiveness of the MC-FCS solver and to evaluate its computational efficiency. Numerical results show that: the MC-FCS solver has been correctly implemented; the MC-FCS method is highly effective in remedying ray effects; and computational efficiency of MC-FCS is acceptable, especially considering the great improvement in solution accuracy it can bring.