A MOC-based heterogeneous leakage model

This paper presents some developments of the APOLLO3${}^{\text{®}}$code and their applications in support to industrial studies. We describe a numerical technique to implement, in the framework of the Method Of Characteristics (MOC), the Heterogeneous Leakage Model (HLM). We preliminarily set up the theoretical framework of this model and clarify some aspects related to its use as homogenization technique that we believe important. In fact in the classic use of HLM for homogenization some important approximations are made to switch from complex-valued fluxes to real-valued weighting functions. We suggest an approach to avoid such approximations in practice. Then we describe a new numerical technique to solve with the MOC the HLM. The approach consists in integrating the complex-valued leakage term of the HLM directly in the cross section, and therefore to generalize MOC by integrating a complex-valued function. Moreover we detail also the necessary modifications that are necessary to adapt the classical algorithm of critical search (valid for the classical $D{B}^2$ leakage model) to the new context. Numerical results are shown in support to these developments.