Lattice Boltzmann method for Nuclear Reactor Physics Hitesh Bindra CUNY Energy Institute, 160 Convent Ave., New York, NY, 10031, Email: hbindra@che.ccny.cuny.edu INTRODUCTION Most of the nuclear reactor physics problems involving neutron or radiation transport are described by linear Boltzmann transport theory. These transport theory based problems are either solved by Monte Carlo methods or deterministic methods with fixed angular discretization. The grid or mesh used in the deterministic methods is restricted by the use of discrete angular directions. Whereas, the fluid dynamics, solid mechanics or material modeling tools which are commonly used, are finite volume or finite element based. It is therefore difficult to solve multi-physics coupled problems involving neutron transport theory and material or fluid dynamics in single grid framework without large amount of additional processing or introducing additional approximations. Bindra et. al. [1] proposed a convenient method for solving neutron or radiative transport problems using Lattice Boltzmann Method (LBM). The popular use of LBM is seen in fluid mechanics, where the general Boltzmann equation is solved which has non- linear term in the collision kernel or integral part of the equation. Therefore, it is a natural choice to be used for solving linear form of Boltzmann equation i.e. neutron transport equation as well. The LBM is similar to discrete ordinate methods in formulation but is simpler in implementation (see Ref. [1] for details) and can be adopted for structured or arbitrary grid framework. The Lattice Boltzmann and discrete ordinate methods differ in the use of angular discretization schemes, which makes LBM more suitable for different types of grids. LBM has other additional advantages, such as substantially less numerical dispersion error, ease of parallelization etc. over conventional difference schemes [2,3]. The LBM for fluid mechanics and multi-phase simulations have already been developed for several fluid mechanics and thermal- hydraulics applications. Therefore, using LBM for neutronics will provide a single framework to solve coupled problems in neutronics and thermal-hydraulics. Although, recently developed tools such as MOOSE [4] have the capability to treat multi-physics in the single grid, the LBM is a common numerical scheme for solving linear or non-linear forms of Boltzmann equation representing neutronics and fluid mechanics respectively. LBM also has inherent advantage and is being used preferentially in handing -- two-phase flows and boiling, which are commonly encountered problems in nuclear engineering, over conventional CFD methods. Therefore, neutronics LBM code will provide additional benefit of compatibility with anticipated next generation thermal- fluid solvers. In this summary, we will present the LB method and show its implementation in the basic problem of reactor physics that is criticality estimation in two region slab geometry. DESCRIPTION OF THE METHOD Previously, general purpose formulation of Lattice Boltzmann method for solving transport equations with scattering term was presented [1]. This formulation was demonstrated for both isotropic and anisotropic scattering problems and results were verified with other existing methods such as harmonic expansion (P n ) and discrete ordinate (S n ) methods. These problems had volumetric source term or boundary influx. Here, we will use the same method to demonstrate the implementation of LB method for reactor criticality search problems. Criticality problems are approached by converting the problem into eigenvalue problem and then finding the solution for those eigenvalues [5]. Criticality problems, because of their importance in nuclear engineering, have always been used as initial tests for novel numerical techniques and large database of such problems exist in the literature [6] for performing such tests. The mono-energetic time- independent neutron transport equation with the fission term can be written as (1) ) , ( ) , ( 4 ) , ( ) ( 4 1 ) , ( ) , ( . 4 4                        r Q d r d r r r f s           (1) where,  is the neutron flux at spatial location r in the  direction,  is the total neutron cross-section, s  is the scattering cross-section, f  fission cross-section,  is the number of neutrons generated per fission and Q is the neutron source. The LB equation to numerically solve equation (1) can be written as (2), based on the original LB equation derived for general transport equation in Ref. [1].