Adjusted Levermore–Pomraning equations for diffusive random systems in slab geometry. (March 2015)

• Record Type: Journal Article
• Authors: Vasques, Richard; Yadav, Nitin K.
• Is Part Of: Journal of quantitative spectroscopy & radiative transfer. Volume 154(2015:Apr.)
• Page Start: 98
• Page End: 112
• Publication Date: 2015-03
• Subjects: Particle transport -- Levermore–Pomraning -- Random media -- Diffusion; Spectrum analysis -- Periodicals; Radiation -- Periodicals; Analyse spectrale -- Périodiques; Rayonnement -- Périodiques; Radiation; Spectrum analysis; Periodicals; 543.0858
• DOI: 10.1016/j.jqsrt.2014.12.012
• Languages: English
• ISSNs: 0022-4073

Abstract

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, 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. Abstract : Highlights: 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.