Derivation of a Non-Local Model for Diffusion Asymptotics — Application to Radiative Transfer Problems
Year: 2010
Communications in Computational Physics, Vol. 8 (2010), Iss. 5 : pp. 1139–1182
Abstract
In this paper, we introduce a moment closure which is intended to provide a macroscopic approximation of the evolution of a particle distribution function, solution of a kinetic equation. This closure is of non-local type in the sense that it involves convolution or pseudo-differential operators. We show it is consistent with the diffusion limit and we propose numerical approximations to treat the non-local terms. We illustrate how this approach can be incorporated in complex models involving a coupling with hydrodynamic equations, by treating examples arising in radiative transfer. We pay a specific attention to the conservation of the total energy by the numerical scheme.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.211009.100310a
Communications in Computational Physics, Vol. 8 (2010), Iss. 5 : pp. 1139–1182
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 44
-
Telescopic Projective Integration for Linear Kinetic Equations with Multiple Relaxation Times
Melis, Ward | Samaey, GiovanniJournal of Scientific Computing, Vol. 76 (2018), Iss. 2 P.697
https://doi.org/10.1007/s10915-017-0635-0 [Citations: 6] -
Projective and telescopic projective integration for the nonlinear BGK and Boltzmann equations
Melis, Ward | Rey, Thomas | Samaey, GiovanniThe SMAI journal of computational mathematics, Vol. 5 (2019), Iss. P.53
https://doi.org/10.5802/smai-jcm.43 [Citations: 8] -
A High-Order Asymptotic-Preserving Scheme for Kinetic Equations Using Projective Integration
Lafitte, Pauline | Lejon, Annelies | Samaey, GiovanniSIAM Journal on Numerical Analysis, Vol. 54 (2016), Iss. 1 P.1
https://doi.org/10.1137/140966708 [Citations: 15] -
Large-Time Behavior of the Solutions to Rosenau-Type Approximations to the Heat Equation
Rey, Thomas | Toscani, GiuseppeSIAM Journal on Applied Mathematics, Vol. 73 (2013), Iss. 4 P.1416
https://doi.org/10.1137/120876290 [Citations: 0] -
On the Spitzer–Härm Regime and Nonlocal Approximations: Modeling, Analysis, and Numerical Simulations
Goudon, Thierry | Parisot, MartinMultiscale Modeling & Simulation, Vol. 9 (2011), Iss. 2 P.568
https://doi.org/10.1137/100800269 [Citations: 3]