A second-order maximum-entropy inspired interpolative closure for radiative heat transfer in gray participating media

Some recent advances on the method of moments in kinetic theory

“…The interpolative closures were developed in the fields of CFD ( [33]) and of radiative transfer ( [32,39,41]). It aimed at reducing the computational costs of the entropy-based closure by using a high order polynomial approximation that interpolates the exact entropy-minimizing closure at specific locations in the realizability domain.…”

Moment methods for the radiative transfer equation based on φ-divergences

“…Even if the exact M N approximation does preserve symmetry in the solution, computing it numerically generally requires an approximation (see typically [18,4,3] for efficient techniques) which eventually violates symmetry. Such a closure can also be computed analytically at order 1 ( [13]) or can be approximated up to order 2 ( [29,39,31,41]), but high order multi-D models remain inaccessible.…”

On the Renormalization Maps for the φ -Divergence Moment Closures Applied in Radiative Transfer

“…Those are efficient, but the first fails at modeling beams, the second requires high computational costs due to need to solve large numbers of (potentially ill-conditioned) optimization problems. Those were an inspiration for many other techniques developed in this field, including the simplified models (Frank et al 2007;McClarren 2010), the flux-limited diffusion (Humbird and McClarren 2017;Olson, Auer, and Hall 2000)), the interpolative methods (Li and Li 2020;Pichard et al 2017;Sarr and Groth 2020) and others (see e.g. Pichard 2020;Schneider 2016).…”