Unstructured Triangular Nodal-SP₃ Method Based on an Exponential Function Expansion

The isotropic simplified spherical harmonics (SP₃) method is employed to cast the neutron transport equation into a coupled set of two equations each of which shares identical mathematical form with the neutron diffusion equation. An exponential function expansion nodal (EFEN) method is presented for an arbitrary triangular grid and implemented to solve the coupled SP₃ equations. The EFEN method couples adjacent nodes by defining partial currents on each interface and expanding the detailed flux distribution within each node into a sum of exponential functions to obtain a response matrix between the incoming and outgoing partial currents and a neutron balance condition for each node to obtain the nodal average flux. Numerical results demonstrate that both k_eff and power distributions agree well with other codes. We find comparable accuracy in most situations, and the new method appears to be faster than the other codes even in cases where EFEN requires a finer unstructured mesh.