Comparison of two three-dimensional heterogeneous variational nodal methods for PWR control rod cusping effect and pin-by-pin calculation

Two heterogeneous nodal methods based on the Variational Nodal Method (VNM) are investigated with diffusion approximation in three-dimensional Cartesian geometry. The first one is named as Function Expansion (FE) method while the second is Finite Sub-element (FS) method. Based on our previous work and the code Violet-Het1D in one-dimensional slab geometry, a code named Violet-Het3D was developed to handle the Pressurized Water Reactor (PWR) control rod cusping effect and pin-by-pin calculation by using either of these two methods. To eliminate the control rod cusping effect, Violet-Het3D provides a different idea from the existing methods. Neither homogenization procedure nor mesh adjustment is needed in Violet-Het3D by taking advantage of the treatment for heterogeneous nodes. Numerical results show that both the FE and FS methods can eliminate the cusping effect and obtain accurate power distribution while the FE method has relatively higher efficiency and accuracy. In contrast, for pin-by-pin calculation, the FS method obtains more accurate eigenvalue and pin power distribution than the FE method.