Study on Unstructured-Mesh-Based Importance Sampling Method of Monte Carlo Simulation

Abstract

Monte Carlo (MC) method is widely adopted in radiation transport calculation due to its high accuracy, but suffers from high variance in deep-penetration problems. To obtain reasonable results, variance reduction techniques are necessary and thus be widely studied worldwide. The Consistent Adjoint Driven Importance Sampling (CADIS) method is proved to be an effective variance reduction technique, which generally employs finite-difference discrete ordinate (SN) code to obtain the adjoint flux, and generates parameters of source biasing and weight window for MC code. However, the finite-difference method, which models through structural meshes, will introduce considerable geometric approximations in complex geometry. The finite element method (FEM) performs calculations with lower truncation error and can employ unstructured meshes, which are capable of modeling complex geometry with relatively lower geometric approximations. Therefore, the adjoint flux calculated by unstructured-mesh FEM is able to generate more appropriate parameters of source biasing and weight window which will further reduce the variance of forward MC calculation. A fully automatic unstructured-mesh CADIS method is studied and implemented in this paper, parallel three-dimensional unstructured-mesh neutron-photon coupled transport calculation code NECP-SUN based on the SN method and discontinuous FEM is developed and embedded into the MC code NECP-MCX to calculate the adjoint flux with unstructured meshes. The updated code is applied to the HBR-2 benchmark, the numerical results show that the relative statistic error is reduced by up to 22% compared to the traditional CADIS method while the calculation results are closer to the measurements and the figure of merit (FOM) is increased by 3–4 orders comparing to direct MC simulation.