The source expansion neutron transport discrete ordinates method expresses the solution of differential form discrete ordinates by a sum of polynomial form particular solution and exponential function homogeneous solution. The incoming angular neutron flux can be used as boundary condition to determine the coefficients of homogeneous solution. The particular solution can be obtained directly with source expansion coefficients. Finally, the hexagonal neutron transport equation can be solved with source iteration. Discrete ordinates method normally converges slow and can be accelerated with coarse mesh finite method (CMFD). Numerical results indicates that eigenvalues and power distributions of the reference problems agrees well with reference results. The CMFD acceleration method achieves more than 20 times speedup in the study.

The nodal expansion method (NEM) based on transverse integrated technique is widely used in liquid water reactor core design. It uses an empirical transverse leakage polynomial approximation. Furthermore, it requires pin power reconstruction model for pin power within the assembly. A generic transverse integrate proposed in this work avoids the above shortages. Since the core heterogeneous usually happens in radial direction, the 3D neutron diffusion equation is solved with 2D generic transverse integrate fused with traditional 1D semi-analytical nodal method. With IAEA 2D/3D benchmark problem, the method is demonstrated correct and feasible for core neutron diffusion calculations.