A discrete-ordinates variational nodal method for heterogeneous neutron Boltzmann transport problems

This study introduces an unstructured variational nodal method (UVNM-S N ), also recognized as the hybridized discontinuous Galerkin (HDG) method, for solving heterogeneous neutron Boltzmann transport problems. The UVNM-S N solves the variational formulation of neutron Boltzmann transport equation (NBTE) by meshing the problem domain with non-overlapping nodes, i.e. the meshes. Lagrange multipliers are introduced along nodal interfaces enforcing neutron conservation. The interface unknowns are globally coupled and solved as the Dirichlet data to recover local within-node unknowns. Unstructured meshes are handled using the coordinate transformation technique, while the angular variables are discretized using the discrete-ordinates (S N ) method. Furthermore, within the framework of the UVNM-S N , the nonlinear diffusion acceleration (NDA) is incorporated to tackle the issue of slow convergence of the power iteration (PI). Besides, the volume correction method is developed to facilitate the implementation of the UVNM-S N for heterogeneous problems. The 2D and 3D C5G7 benchmark problems and the SIMONS test problem are utilized to verify the suggested methods. According to numerical results, UVNM-S N exhibits geometric compatibility and precision in a variety of applications. Moreover, the volume correction method yields a speed-up ratio of around 10, and the NDA method provides a 6-12 speed-up ratio.