Performance comparison of zeroth order nodal expansion methods in 3D rectangular geometry

This work presents a study on the performance comparison of zeroth order nodal expansion methods, NEM. A computer code based on zeroth order nodal expansion methods, ZONEM-3D, is developed for the steady state diffusion equation calculation using nodal expansion family methods including average current, average flux, point current and point flux in 3D cubic geometry. The aim of this work is to determine the relative merits of four variants in terms of accuracy per computing time expended. To speed up the solution schemes, we implemented the fission source weighting in the power method procedure. The influence and capability of the accelerating technique are investigated by considering the execution time through solving some test cases. Four popular test problems, BIBLIS-2D, ZION-2D PWR reactor benchmark, LMW LWR-3D and IAEA-3D benchmark, are used to assess the performance comparison of the methods. Overall, numerical results demonstrate although the accuracies of all methods are adequate but point methods are the most accurate of four variants on considered problems and have relatively higher accuracy than average methods by using coarse meshes. In contrast, execution time of average methods is less than point methods because of having less computational efforts. Also we find current methods have less execution time relative to flux methods. For surveying the influence of considered acceleration method, several fission source weightings are considered and investigated.