Discrete Ordinates Numerical Integration Method for Neutron Transport Equation in Slab Geometry

On discontinuous Galerkin and discrete ordinates approximations for neutron transport equation and the critical eigenvalue

Massively Parallel Cartesian Discrete Ordinates Method for Neutron Transport Simulation. (SN cartésien massivement parallèle pour la simulation neutronique)

High-fidelity nuclear reactor core simulations require a precise knowledge of the neutron flux inside the reactor core. This flux is modeled by the linear Boltzmann equation also called neutron transport equation. In this thesis, we focus on solving this equation using the discrete ordinates method (SN) on Cartesian mesh. This method involves a source iteration scheme including a sweep over the...

Sparse Discrete Ordinates Method in Radiative Transfer

The stationary monochromatic radiative transfer equation (RTE) is a partial differential transport equation stated on a five-dimensional phase space, the Cartesian product of physical and angular domain. We solve the RTE with a Galerkin FEM in physical space and collocation in angle, corresponding to a discrete ordinates method (DOM). To reduce the complexity of the problem and to avoid the “cu...

Multilevel Source Iteration Accelerators for the Linear Transport Equation in Slab Geometry

In this paper we show how classical error estimates for various discretiza-tions of the source iteration map in slab geometry can be used to construct accurate approximate inverses in the context of fast multilevel methods. For discretizations that give strongly convergent collectively compact sequences of approximate source iteration maps, the Atkinson-Brakhage approximate inverse can be appli...

The Green’s function for the radiative transport equation in the slab geometry

Abstract The radiative transport equation is solved in the three-dimensional slab geometry by means of the method of rotated reference frames. In this spectral method, the solution is expressed in terms of analytical functions such as spherical harmonics and Wigner d-functions. In addition, the eigenvalues and eigenvectors of a tridiagonal matrix and certain coefficients, which are determined f...