A hybrid method for the solution of linear Boltzmann equation

• The paper presents a novel method for the solution of linear Boltzmann equation.
• The hybrid method, based on multiple collisions, combines transport with diffusion.
• The physical basis of the method is discussed together with the mathematical model.
• Results show its performance in terms of accuracy and computational time.
• The extension of the method to more general configurations is discussed.

This paper presents a novel approach devised to solve the transport of neutral particles in scattering and absorbing media. The solution to the linear Boltzmann equation is sought starting from a multi-collision approach of the integro-differential equation which is combined with an approximate model for the description of the residue after truncation of the Neumann series. In the paper, the theoretical basis of such hybrid method is discussed together with the physical intuition at the basis of the methodology. Results for both steady-state and transient problems are presented and an extension to general multi-dimensional, anisotropic problem is reported.