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

Abstract

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.

V.2.: We have added around 7 pages of new text; three new sets of numerical results; 6 new figures; and two new references [13, 17]. Current version has 18 pages, 10 figures. The changes correspond to an expansion of Sections 3 and 4. Section 3 now has more detailed and complete analysis; Section 4 has new numerical results