Variant of Green's Function Nodal Method for Neutron Diffusion

Abstract

A variant of the Green's function nodal method derived from the boundary integral form of the multigroup neutron diffusion equation in rectangular geometry is presented. As usual in the nodal methods, the multi-dimensional diffusion equation is integrated in the transverse direction. The resulting 1D diffusion equation is solved following the Boundary Element technique in one dimension. In this way a weighted residual method is obtained, with a Green's function for weighting, but with different boundary conditions than normally applied in the Green's function nodal methods. Mathematical formulation of the method is given and the iteration procedure is described. A computer program BINDIF has been designed, based on the new method. Its capabilities include the solution of the multigroup neutron diffusion equation of ID, 2D and 3D rectangular lattices. The BINDIF program has been checked against other methods used for global reactor calculations on benchmark problems, representative of realistic power reactor cores. The results indicate that the method is attractive to design highly efficient algorithms for a large mainframe, a personal computer or a parallel processor.

KEYWORDS:

• neutron diffusion equation
• multigroup theory
• power distribution
• multiplication factors
• coarse mesh method
• nodal method
• Green function
• computer codes
• computer calculations