Development and implementation of an integral variational nodal method to the hexagonal geometry nuclear reactors

Abstract

This paper presents recent progress of the development and implementation of the integral transport variational nodal method (VNM) to the neutronics modelling of hexagonal geometry nuclear reactors. In this study, the three-dimensional multi-group neutron transport equation is solved with the variational nodal method utilizing an integral form of the with-in node angular flux distribution to generate response matrices more efficiently. The angular flux distributions on hexagonal nodal interfaces are approximated with even-parity spherical harmonics. The quasi-reflected interface condition (QRIC) method is employed to reduce the number of interfacial angular terms to save computational costs. Parallelization algorithms are accounted to accelerate the response matrix formation process. The newly-implemented methods are examined against the TAKEDA-4 benchmark cases, presenting superior accuracy and efficiency than the standard VNM approach. With the P7 angular approximation, the joint performance of the integral method and the QRIC method yields a remarkable computational time gain of 33.0. Furthermore, an 11-core parallelization to the response matrix formation process results in another 88% reduction in the total computation time.