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Title: On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models

The unified gas kinetic scheme (UGKS) of K. Xu et al. (2010) [37], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of radiative transfer theory. While such problems exhibit purely diffusive behavior in the optically thick (or small Knudsen) regime, we prove that UGKS is still asymptotic preserving (AP) in this regime, but for the free transport regime as well. Moreover, this scheme is modified to include a time implicit discretization of the limit diffusion equation, and to correctly capture the solution in case of boundary layers. Contrary to many AP schemes, this method is based on a standard finite volume approach, it does neither use any decomposition of the solution, nor staggered grids. Several numerical tests demonstrate the properties of the scheme.
Authors:
 [1] ;  [2] ;  [2]
  1. Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence (France)
  2. (France)
Publication Date:
OSTI Identifier:
22230821
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 253; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; BOUNDARY LAYERS; DECOMPOSITION; DIFFUSION; DIFFUSION EQUATIONS; RADIANT HEAT TRANSFER; TRANSPORT THEORY