Development of a high order and multi-dimensional nodal code, ACNEC3D, for reactor core analysis

Abstract The aim of this work is to develop a coarse mesh code using various orders of average current nodal expansion method to solve the neutron balance equation implementing the proposed adopted iterative solution algorithm for reactor core calculations. Modern nodal methods have the ability to treat diffusion equation with coarse meshes which cause the considerable reduction of CPU memory and computational costs. A major cause of errors in the calculations is the existence of high flux gradient in some nodes. These errors can be decreased by increasing the order of solution and/or decreasing the mesh sizes. A program based on Average Current Nodal Expansion Code, ACNEC3D, has been developed to solve multi group diffusion equation in three dimensional rectangular geometries using zeroth, first and second orders of average current nodal expansion method. Some popular benchmarks have been investigated and results of various orders of solutions and mesh sizes are compared with reference solutions. Results indicate when the order of solution is increased or/and mesh sizes are decreased, the accuracy of solution is enhanced. According to the results, second order solution has adequate accuracy and higher efficiency in calculations with coarse meshes equal to the dimensions of a FA. Moreover, results show the most of major errors are appeared in peripheral FAs because of flux gradient existence between FAs and reflectors. As a result, more error reductions are taken place in these regions which cause the improvement of accuracy.