Numerical comparison between two spherical harmonics expansion models and a kinetic equation

In this paper, we investigate the reliability of two diffusion models, the SHE andcoupled SHE models, by accurate numerical comparisons with a Boltzmann-like equation. These models describe the transport of particles subject to collisions with the medium. Comparisons are given at three levels of description: at small times (transient regime), at the diffusion time (diffusion regime), and for long times (stationary regime). The three regimes are well described by both SHE models. A discussion of the main benefits and drawbacks of each of the SHE models is given, according to the regime.