Generalized Integral Method for Solving the Neutron Transport Equation with the Hybridized Discontinuous Galerkin Method

Accurate modeling of the neutron transport equation (NTE) with anisotropic scattering is crucial to the understanding of neutron interactions within various mediums. The primary challenges in this domain are (1) the considerable computational resources demanded by anisotropic calculations and (2) the numerical instabilities that arise due to the transport correction approximation.

This study introduces a novel, generalized integral method based on the hybridized discontinuous Galerkin framework for solving the second-order NTE with anisotropic scattering. This method employs a spherical harmonics expansion to define the partial current at the mesh interface and applies an angular integral approach to the flux treatment within the mesh. This dual approach facilitates an efficient computational process while preserving accuracy.

The integral method has been validated through comparisons with the standard discrete ordinates method (S_N) using two eigenvalue problems. The integral method showcases several significant improvements over the traditional S_N method. First, it repositions the P₀ scattering sources during the formulation process, effectively circumventing the convergence issues associated with transport correction. Second, this strategic repositioning substantially enhances the convergence rates of iterative calculations. Last, a standout feature of the integral method is its capability to perform angular integrals during assembling matrices, successfully reducing the floating-point operations for local flux retrieval and eliminating the ray effect.