The ℓ-distribution method for modeling non-gray absorption in uniform and non-uniform gaseous media

•The ℓ-distribution modeling is introduced.•It achieves LBL accuracy in uniform media.•It is as accurate as usual C-k models in non-uniform media.•Its computational cost is lower than k-distributions.

The ℓ-distribution modeling is proposed for radiative heat transfer in uniform and non-uniform non-gray gaseous media. The method is partly based on the application of results from the k-moment method. It combines this technique with several concepts from probability theory: the notion of rank transmutation maps allows extending the k-moment method to an infinite number of k-moments; copula models appear naturally to extend the method from uniform to non-uniform gas paths. The ℓ-distribution approach is shown to provide results: (1) more accurate - up to three orders of magnitude - than usual k-distribution approaches in uniform media, (2) as precise as correlated-k models in non-uniform situations. All these results are obtained at a computational cost lower than k-distribution models. Differences and similarities between k- and ℓ-distribution methods are discussed.