Computation of the uncollided-flux moments with advanced MOC and QP methods

Abstract

The growing need to solve radiation protection and shielding problems in reasonable computational times has led to an increasing interest in the use of deterministic approaches. Codes of this type commonly use the discrete-ordinates method. In cases of propagation of point sources in low scattering media, which are typical of shielding studies, the approximation leads to a set of numerical artefacts known as ray effect. One of the most commonly used techniques to mitigate this effect is the calculation of the uncollided flux, which is the most affected flux component, with a fine transport operator. In this paper we propose four different approaches: the method of characteristics (MOC), the trajectory-splitting MOC (TS-MOC), the Monte Carlo MOC (MC-MOC) and the method based on quadrature points (QP). They have been implemented inside the Cartesian solver IDT. This paper contains the formal description of the four numerical methods and their verification over a set of benchmark problems. An analysis of the accuracy and the computation performances of the methods is also given. Finally, a comparison of the four methods on the Kobayashi benchmark problem is proposed.