Asymptotic Expansion of the Angular Flux Applied to Discrete-Ordinates Source Iterations in Lattice Depletion Calculations

Abstract

This work presents an asymptotic method based on angular flux expansion in a Neumann series. The technique is aimed at effective reduction of the memory imprint of numerical methods based on collision probabilities (CPs). The asymptotic method has been implemented in the heterogeneous Cartesian cells of the integro-differential transport solver (IDT). The IDT solves the neutral-particle transport equation by discrete ordinates combined with angular-dependent CP matrices. In lattice depletion calculations, because of the change of isotopic concentration along the burnup, methods based on CP discretization, such as current-coupling CP or the one presented in this paper, would require construction and storage of a set of CP coefficients for any depleted pin cell. When the number of media grows, the performances of the solver are bounded by the memory pressure caused by the growth of coefficients. Application of the asymptotic technique, presented in this paper, transforms by two user’s parameters the memory-bound solver in a compute-bound application, where the principal workload is transferred from coefficients to source iterations. In this work, a theoretical study of the method is presented together with two applications to two-dimensional assembly simulations. The effects on self-shielded and depleted materials are highlighted. Preliminary results show an encouraging reduction of memory occupation by a factor 10 without any significant loss of accuracy.