and to the multigroup k-Distribution method [@MOD-ZHA:2001]. We point out that the current approach is able to explicitly handle scattering in energy, which to the best of our knowledge has not been explored with k-Distribution methods.

The remainder of this paper is organized as follows. In Section \[sec:The-homogenized-transport\], we derive the homogenized equations, and their discrete approximation. We then apply we apply the above methodology to three examples in Section \[sec:Examples\]. For simplicity, we neglect scattering in all examples. In Section \[sub:Example-1:-the\], we consider the Elsasser band model (\[eq:Elsasser band model, intro\]) with $\varepsilon=10^{-4}$ (see also [@POMRAN:1971]). For the Elsasser band model, we also analytically compute the Young measure $\lambda_{E}\left(\xi\right)$ and compare it with its discrete approximation (\[eq:discrete approx of Young measure, intro\]). In the second example, we consider a neutron transport example using an absoption cross section $\sigma_{\varepsilon}\left(E\right)$ for iron at room temperature and a Watt fission spectrum; note that, in this case, the subscript $\varepsilon$ of $\sigma_{\varepsilon}\left(E\right)$ is formerly retained in order to denote the characteristic resonance spacing, but is not an actual free parameter. Finally, in our last example, we consider an atmospheric TRT calculation; we use $12$ homogenous atmoshperic layers between $1\,$km-$12\,$km (the temperature and pressure 