Source Expansion Nodal Solution of SP3 Equations with P1 Coarse Mesh Finite Difference Formulation

In order to effectively account for the transport effects in core calculations, the SP3 equations are adopted in some of the existing nodal diffusion codes such as PARCS and DYN3D. The advantage of using the SP3 equations comes from the similarity between the SP3 equations and the diffusion or P1 equation that make it possible to use the existing code's architecture and solution methods that were developed for the nodal diffusion equation. The only difference is that there are one more balance equation and one additional unknown, the second angular moment. For the solution of the SP3 equations by the nodal method, the nodal expansion method was first developed and the source expansion nodal method(SENM) was introduced as an accurate kernel to capture correctly the drastic variation of the second angular moment near material interfaces. The exponential part of the source expansion nodal solution turned out to be very effective in describing the strong gradient in the second angular flux near the surface and this capability of SENM provides better accuracy than the corresponding NEM solution. On the other hand, a nodal solution kernel can be formulated locally employing either a one-node or two- node formulation. The one-node formulation requires incoming current conditions while the two-node formulation requires node average fluxes. In principle, these boundary conditions can be provided by the global coarse mesh finite difference (CMFD) solution that includes both zero-th and second angular moment fluxes. Inclusion of the second angular moments in the CMFD system, however, can lead to potential instability because of the large gradient of the second angular moments near each interface. This work is to develop a way not to use the second angular moment in the CMFD equation by keeping the ordinary P1 CMFD formulation