On the Asymptotic Preserving property of the Unified Gas Kinetic Scheme for the diffusion limit of linear kinetic models
Language
en
Article de revue
This item was published in
Journal of Computational Physics. 2013, vol. 253, n° 15, p. 138-156
Elsevier
English Abstract
The unified gas kinetic scheme (UGKS) of K. Xu et al. [K. Xu and J.-C. Huang, J. Comput. Phys., 229 , pp. 7747--7764, 2010], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear ...Read more >
The unified gas kinetic scheme (UGKS) of K. Xu et al. [K. Xu and J.-C. Huang, J. Comput. Phys., 229 , pp. 7747--7764, 2010], 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.Read less <
English Keywords
Transport equations
diffusion limit
asymptotic preserving schemes
stiff terms
Origin
Hal imported