A linearization method for the transverse-leakage terms in hexagonal nodal method based on the conformal mapping technique

Widely used in the hexagonal-assembly core-analysis code, the conformal mapping technique has proved to be suitable, accurate, and efficient. Throughout the years of its fledging development, there was hardly any treatment generally applicable for the conformally mapped transverse-leakage terms. This issue notably affected the calculation accuracy of the hexagonal nodal calculation. To address this issue, in the present study, a linearization method for the transverse-leakage terms has been proposed, which estimates the current distribution of nodal surfaces with corresponding flux distribution on surfaces adjacent to neighboring nodes. This method provides an accurate distribution of the transverse-leakage terms, leading to calculation results with high accuracy. The proposed method has been implemented in our in-house core-analysis code, SPARK, enabling the solution of the three-dimensional multi-group neutron-diffusion equation using hexagonal nodes. To verify the method, the two-dimensional VVER-1000 benchmark problem was calculated in the first place. Compared with the conventional flat-current assumption, the proposed linearization method decreased the error of eigenvalue and the maximum error of the nodal normalized power from 62.9 pcm to 8.6 pcm and from 5.60% to −0.65%, respectively. Subsequently, numerous 2D/3D benchmarks were modeled and verified, comparing the eigenvalues and assembly-averaged power distributions with their corresponding reference values. The numerical results indicate that the proposed linearization method performs satisfactorily, reducing the maximum error in eigenvalue to about 20.0 pcm and keeping the errors in power distribution below 0.9%. As a result, the proposed linearization method significantly improves computation accuracy and offers an effective solution for handling the transverse-leakage terms using the conformal mapping technique.