An AFEN Equivalent Hexagonal Nodal Method based on the Single-Node Nonlinear FDM Response Matrix

The flux moments which are defined by the weighted average fluxes at the interface are used as nodal unknowns corresponding to the added basis functions. A linear function or a step function in parallel to the interface direction is used as a weighting function. On the other hand, the corner point fluxes are no longer used as nodal unknowns, since it is expected that sufficient accuracy can be achieved even without them. According to Reference 5, the refined AFEN method even without corner point fluxes provides much better accuracy than the original AFEN method. In addition, the nodal method employs a response matrix method that uses the interface partial currents as nodal unknowns instead of the interface fluxes used in the original AFEN method. The response matrix method updates the outgoing partial currents of each node at each inner iteration step by imposing the incoming partial current boundary conditions on the interfaces of the node. This paper reports the preliminary results of applying this method to a two-dimensional benchmark problem to evaluate its applicability to practical core analysis. In order to improve efficiency of the CAPP code in the analysis of the HTGR core, a nonlinear FDM-based response matrix method in the hexagonal geometry has been developed in a manner that it is equivalent to the refined AFEN method. In the nodal method, the corner point fluxes are no longer nodal unknowns, but the flux moments which are defined by the weighted average fluxes at the interface take the role of nodal unknowns. In addition, the method adopts a two-factor coarse-mesh finite difference (CMFD) nonlinear iteration as in Reference 6. It solves the single node problem by the AFEN method to determine the interface nonlinearity correction factors instead of the two-node problem as utilized in Reference 6.