Radiative or neutron transport modeling using a lattice Boltzmann equation framework

Abstract

In this paper, the lattice Boltzmann equation (LBE)-based framework is used to obtain the solution for the linear radiative or neutron transport equation. The LBE framework is devised for the integrodifferential forms of these equations which arise due to the inclusion of the scattering terms. The interparticle collisions are neglected, hence omitting the nonlinear collision term. Furthermore, typical representative examples for one-dimensional or two-dimensional geometries and inclusion or exclusion of the scattering term (isotropic and anisotropic) in the Boltzmann transport equation are illustrated to prove the validity of the method. It has been shown that the solution from the LBE methodology is equivalent to the well-known P(n) and S(n) methods. This suggests that the LBE can potentially provide a more convenient and easy approach to solve the physical problems of neutron and radiation transport.