Multilevel method to compute the lambda modes of the neutron diffusion equation

Determination of the reactor kinetic characteristics is very important for the design and development of a new reactor system. In this sense, the computation of lambda modes associated to a nuclear power reactor has interest since these modes can be used to analyze the reactor criticality and to develop modal methods to analyze transient situations in the reactor. In this paper, the lambda problem has been discretized using a high order finite element method to obtain a generalized algebraic eigenvalue problem. A multilevel method is proposed to solve this generalized eigenvalue problem combining a hierarchy of meshes with a Modified Block Newton method. The Krylov-Schur method is used to compare the efficiency of the multilevel method solving several benchmark problems.

Lattice Boltzmann Method for Solving Time-Dependent Radiation Transport and Reactor Criticality Problems

The recently developed lattice Boltzmann equation (LBE) framework [1] for radiation transport is extended to solve time-dependent nonequilibrium neutron transport problems. Dynamics of radiation and material energy exchange is modeled by coupling the radiation transport equation with the material energy equation in a one-dimensional isotropically scattering homogenous medium. The LBE equations are obtained for corresponding radiative or neutron transport in constant source and reactor criticality search problems. Furthermore, a two-dimensional D2Q8 & D2Q16 LBEs are proposed for solving the time-dependent neutron transport equation in a heterogenous media (e.g., a checkerboard lattice with pure scattering and absorbing cells). The results obtained with LBE are in good agreement with the existing discrete ordinate method results for the benchmark problem.