Adjusted Levermore-Pomraning equations for diffusive random systems in slab geometry

This paper presents a multiple length-scale asymptotic analysis for transport problems in 1-D diffusive random media. This analysis shows that the Levermore-Pomraning (LP) equations can be adjusted in order to achieve the correct asymptotic behavior. This adjustment appears in the form of a rescaling of the Markov transition functions by a factor $\eta$, which can be chosen in a simple way. Numerical results are given that (i) validate the theoretical predictions; and (ii) show that the adjusted LP equations greatly outperform the standard LP model for this class of transport problems.