Radiative or neutron transport modeling using a lattice Boltzmann equation framework

Area of Science:

• Computational physics
• Numerical methods

Background:

• The linear radiative and neutron transport equations are fundamental in various physics and engineering fields.
• Solving these equations, especially with scattering terms, can be computationally intensive using traditional methods.

Purpose of the Study:

• To introduce and validate a lattice Boltzmann equation (LBE)-based framework for solving linear radiative and neutron transport equations.
• To demonstrate the efficacy of the LBE framework for problems involving scattering terms (isotropic and anisotropic).

Main Methods:

• The study employs the lattice Boltzmann equation (LBE) framework, adapted for the integrodifferential form of the transport equations.
• Interparticle collisions are neglected, simplifying the model by omitting nonlinear collision terms.
• One- and two-dimensional test cases, with and without scattering, are used to validate the LBE approach.

Main Results:

• The LBE framework successfully solves the linear radiative and neutron transport equations.
• Solutions obtained via the LBE methodology are shown to be equivalent to those from established P(n) and S(n) methods.
• The method's validity is demonstrated across various geometries and scattering conditions.

Conclusions:

• The lattice Boltzmann equation (LBE) framework provides a viable and potentially more convenient alternative for solving neutron and radiation transport problems.
• This method offers a promising direction for computational efficiency and ease of implementation in transport simulations.