Coupled hp-adaptivity for average current nodal expansion method in 2-D rectangular geometry

In this work, we developed an adaptive hp-refinement strategy for average current nodal expansion method in order to solve the neutron balance equation. A flux gradient based a posteriori estimation scheme has been utilized for searching the nodes with numerical errors. The relative Cartesian direction net leakage of nodes has been considered as an assessment criterion. In the algorithm, a fraction of nodes with higher net leakage is selected for more refinement by h-type with splitting to more elements locally and others by p-refinement solution in which the order of solution is increased in the corresponding Cartesian directions. For two test cases, our proposed approach has been investigated. Implementing the proposed adaptive solution indicates that the accuracy of treatment enhances greatly in comparison to using uniform mesh along higher order expansion for flux calculation. Furthermore, results show that the h-refinement approach is suitable for periphery regions around the core due to high flux gradient existence and p-refinement is appropriate for zones with smooth solution such as interior regions.

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