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.

Coupled radiative and conjugate heat transfer in participating media using lattice Boltzmann methods

“…The LBE for a general three dimensional system was modified by Bindra et al [20] to incorporate weighted summations for scattering integrals. Using the taylor series expansion on these discrete LBEs, it can be shown that these equations are first order accurate in space and time.…”

“…(16)), with additional term g @w @sy , where g is the directional cosine in second dimension. The separate physics of radiative heat transfer in two dimensions was modeled using D 2 Q 4 LBM in the previous work [20] for uniform (constant) temperature everywhere in the domain and the results compared well against the S 2 DOM solutions. The …”

“…However, most of the effort was focused on coupling Discrete Ordinates Method (DOM) or other conventional deterministic methods for solving RTEs with the LBM based fluid transport or convection-diffusion solvers [13][14][15][16]. Recently, LBM based algorithms have been developed to solve RTE problems [17][18][19][20][21][22]. This paper proposes the use of those LBM algorithms for solving coupled multi physics examples.…”

Lattice Boltzmann method for solving non-equilibrium radiative transport problems

“…The lattice Boltzmann equation (LBE) method is a relatively new mesoscopic kinetic approach that can provide such a single solver framework. Recently, a LBE approach was developed [1] to solve the steady state radiation transport problems in one and two dimensions. Results for a D 2 Q 4 lattice-equivalent to discrete ordinates S 2 method for time-independent problems-were presented in that work [1].…”

Transient Radiative Transfer in a Graded Index Slab with Fresnel Surfaces

“…This surge in applications of the LBM is owing to its attractive properties of simple implementation on the computer, mesoscopic nature, ability to handle complex geometry and boundary conditions, and the inherent parallel nature. Recently, the LBM itself has been adopted for solving radiation transport problems [22][23][24][25]. However, the graded index medium with the vacuum-medium Fresnel surface has not been included yet.…”