A Reformulation of the Transport-Transport SPH Equivalence Technique

Abstract

The superhomogénéisation (SPH) equivalence technique is a correction procedure based on equivalence factors. These equivalence factors are computed in such a way that a macro calculation made over a macro region and a coarse energy group with a simplified transport operator leads to the same leakage and reaction rates as a reference calculation performed without homogenization and with a fine group discretization. The situation where the macro calculation is performed with diffusion theory is a well understood and a common application of the technique. However, the case where the macro calculation is performed in transport theory is more complex and the SPH technique was reformulated in order to take into account the angular parity of the flux moments and cross sections. We found that the general rule to multiply all cross sections by a SPH factor and to divide all flux moment by the same factor is not valid. A new correction strategy is proposed to deal with transport-theory macro calculations. The strategy is slightly different whether or not the macro calculation is performed with a spherical harmonics (PN or SPN) discretization. The new approach was implemented in the DRAGON lattice code. Numerical results are comparing the classical and reformulated techniques.