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

TL;DR

This paper introduces an adjusted version of the Levermore-Pomraning equations for 1-D diffusive random media, improving their asymptotic accuracy and numerical performance in transport problems.

Contribution

The paper proposes a simple rescaling of the Markov transition functions in LP equations to achieve correct asymptotic behavior in diffusive random systems.

Findings

Adjusted LP equations outperform standard LP models in numerical tests.

Theoretical analysis confirms the asymptotic correctness of the adjustment.

Numerical validation supports the effectiveness of the proposed modification.

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.