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

- We present an asymptotic analysis for the transport equation in 1-D diffusive media.
- We show that the Levermore-Pomraning (LP) model has the wrong asymptotic behavior.
- We propose a set of Adjusted LP (ALP) equations for 1-D diffusive media.
- We show that the ALP equations outperform the LP model in the diffusive systems.
- We present numerical results that validate the theoretical predictions.

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, which can be defined 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.