Three-Dimensional Heterogeneous Variational Nodal Method for PWR Pin-by-pin Calculation and Control Rod Cusping Effect

The Variational Nodal Method (VNM) is generalized for heterogeneous node by using finite sub-element technique within diffusion approximation in three-dimensional Cartesian geometry. Based on the code Violet-Het1D, a code named Violet-Het3D was developed to carry out Pressurized Water Reactor (PWR) pin-by-pin calculation and to handle the PWR control rod cusping effect. Instead of homogenizing the entire heterogeneous node caused by the partially inserted control rods, it explicitly describes the nodal heterogeneity by using tetrahedral mesh. Numerical results demonstrate its high accuracy for the pin-by-pin problem. For the control rod cusping effect, it shows better accuracy and efficiency than the flux-volume-weighted scheme.