Block Radial Basis Function Collocation Meshless method applied to steady and transient neutronics problem solutions in multi-material reactor cores

In nuclear system design, the neutron diffusion equation (NDE) is always used for steady and transient neutron behaviors simulation and in many types of nuclear reactor systems, the whole reactor core consists of several to hundreds of fuel assembles (FAs). In this paper, the Block Radial Basis Function Collocation Meshless (BRBFCM) method is specially developed based on local and global RBFCM method to solve the NDE in nuclear core scale. The whole calculation domain is divided into several blocks according to the FA arrangement and node collocation is used for spatial discretization. Five neutronics benchmark problems are analyzed, including the 2D2G, 2D4G, 2D-IAEA, 2D-TWIGL and 4G-LMFBR problem. The calculation results and the reference values are agreed well, which demonstrates that the more convenient BRBFCM method can solve neutronic problems accurately. Besides, the comparison between BRBFCM, LRBFCM and GRBFCM shows that the BRBFCM has the advantages both on accuracy and efficiency.