An augmented source method for the application of nodal equivalence theory

In most problems of practical interest, the application of Nodal Equivalence Theory (NET) does not disrupt the standard iterative methods used to solve the multigroup nodal equations. However, as we reported earlier, the modular high-temperature gas-cooled reactor (MHTGR) core contains very steep flux gradients, and the application of NET requires large discontinuity factors (DFs) (e.g., partial current DFs larger than 10). These large factors can result in the divergence of the iterative methods used for matrix inversion. Previous investigations into practical methods for overcoming the problem have proven unsatisfactory. Bounding the DFs did not always result in an improved flux solution, and direct inversion methods did not appear to be practical for the general class of problems. In this paper, we discuss the Augmented Source Method (ASM) that accommodates a DF of any magnitude and yet allows use of the standard iterative methods for solving the multigroup nodal equations. The method is based on the concept of treating the DFs as a surface source rather than as a multiplier of the group constants. Because the DFs are introduced to correct the net leakage at each surface of the homogeneous solution, there appears to be some physical basis for introducing neutron sources at the surfaces of each node to ASM within the framework of the Nodal Expansion Method (NEM), but the method is easily adaptable to any form of the nodal diffusion equations. We also provide results of applying the method using the advanced nodal code DIF3D