Analytic Function Expansion Nodal Method for Multigroup Diffusion Equations in Cylindrical (r,,z) Geometry

A coarse-mesh nodal method in cylindrical (r, ,z) geometry, e.g., of pebble bed reactors, based on the analytic function expansion nodal (AFEN) methodology, is described in this paper. Two unique features are (a) no use of transverse integration - allowing a nodal scheme in (r, ,z) geometry - and (b) nodal solution expressed in terms of analytic basis functions - leading to high accuracy and readily available reconstruction of homogeneous flux distributions. Additional features of multigroup formulation, two methods of void region treatment, and coarse-group-rebalance acceleration are implemented in the TOPS code and tested on several benchmark problems, including the Organisation for Economic Co-operation and Development/Nuclear Energy Agency PBMR-400 Benchmark Problem. The TOPS results are in excellent agreement with those of the VENTURE code, using significantly less computer time.