Multigroup neutron transport. II. Half range

Half-space General Multigroup Transport Theory*

A method for solving various half-space multigroup transport problems for the case of a general transfer matrix is explained. A non-linear integral equation for the emergent distribution of the albedo problem is derived. Then, by using the full-range completeness of the infinite medium eigenfunctions, the distribution inside the half-space is obtained from the emergent distribution. Finally, th...

Multilevel NDA Methods for Solving Multigroup Eigenvalue Neutron Transport Problems

The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in one-dimensional slab geometry. The proposed method is defined by a multilevel system of equations that includes multigroup and effective onegr...

Two-group Neutron-transport Theory: Half-range Orthogonality, Normalization Integrals, Applications and Computations

Abstract-A half-range orthogonality theorem concerning the established elementary solutions of the two-group neutron transport equation for isotropic scattering and plane geometry is proved. The orthogonality relations are based on a Chandrasekhar-type H-matrix, and all necessary normalization integrals are evaluated so that the desired expansion coefficients may be expressed concisely in terms...

Three-dimensional h-adaptivity for the multigroup neutron diffusion equations

Adaptive mesh refinement (AMR) has been shown to allow solving partial differential equations to significantly higher accuracy at reduced numerical cost. This paper presents a state-of-the-art AMR algorithm applied to the multigroup neutron diffusion equation for reactor applications. In order to follow the physics closely, energy group-dependent meshes are employed. We present a novel algorith...

Parallel Solvers for the Transient Multigroup Neutron Diffusion Equations