Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-06T02:31:48.015Z Has data issue: false hasContentIssue false
  • English
  • Français

An Implicit Unified Gas Kinetic Scheme for Radiative Transfer with Equilibrium and Non-Equilibrium Diffusive Limits

Published online by Cambridge University Press:  28 July 2017

Wenjun Sun ,
Song Jiang  and
Kun Xu
Wenjun Sun*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Fenghao East Road 2, Haidian District, Beijing 100094, China
Song Jiang*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Fenghao East Road 2, Haidian District, Beijing 100094, China
Kun Xu*
Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong
*
*Corresponding author. Email addresses:[email protected] (W. Sun), [email protected] (S. Jiang), [email protected] (K. Xu)
*Corresponding author. Email addresses:[email protected] (W. Sun), [email protected] (S. Jiang), [email protected] (K. Xu)
*Corresponding author. Email addresses:[email protected] (W. Sun), [email protected] (S. Jiang), [email protected] (K. Xu)
Get access

Abstract

This paper is about the construction of a unified gas-kinetic scheme (UGKS) for a coupled system of radiative transport and material heat conduction with different diffusive limits. Different from the previous approach, instead of including absorption/emission only, the current method takes both scattering and absorption/emission mechanism into account in the radiative transport process. As a result, two asymptotic limiting solutions will appear in the diffusive regime. In the strong absorption/emission case, an equilibrium diffusion limit is obtained, where the system is mainly driven by a nonlinear diffusion equation for the equilibrium radiation and material temperature. However, in the strong scattering case, a non-equilibrium limit can be obtained, where coupled nonlinear diffusion system with different radiation and material temperature is obtained. In addition to including the scattering term in the transport equation, an implicit UGKS (IUGKS) will be developed in this paper as well. In the IUGKS, the numerical flux for the radiation intensity is constructed implicitly. Therefore, the conventional CFL constraint for the time step is released. With the use of a large time step for the radiative transport, it becomes possible to couple the IUGKS with the gas dynamic equations to develop an efficient numerical method for radiative hydrodynamics. The IUGKS is a valid method for all radiative transfer regimes. A few numerical examples will be presented to validate the current implicit method for both optical thin to optical thick cases.

Keywords

02.60.CbRadiative transferasymptotic preservingimplicit methodmultiscale modeling
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 4 , October 2017 , pp. 889 - 912
Copyright
Copyright © Global-Science Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Chen, S.Z., Xu, K., Lee, C.B., and Cai, Q.D., A unified gas kinetic scheme with moving mesh and velocity space adaptation, J. Comput. Phys. 231 (2012), pp. 6643–6664.Google Scholar
[2] Gentile, N.A., Implicit Monte Carlo diffusion - an accerlation method for Monte Carlo time-dependent radiative transfer simulations. J. Comput. Phys., 172 (2001), 543–571.CrossRefGoogle Scholar
[3] Huang, J.C., Xu, K., and Yu, P.B., A unified gas-kinetic scheme for continuum and rarefied flows II: multi-dimensional cases, Communications in Computational Physics, 12, no. 3 (2012), pp. 662–690.Google Scholar
[4] Jin, S. and Levermore, C.D., The discrete-ordinate method in diffusive regimes, Transport Theory Statist. Phys., 20(5-6), (1991), 413–439.Google Scholar
[5] Jin, S., Pareschi, L. and Toscani, G., Uniformly accurate diffusive relaxation schemes for multiscale transport equations, SIAM J. Numer. Anal., 38(3) (2000), 913–936.Google Scholar
[6] Klar, A., An asymptotic-induced scheme for nonstationary transport equations in the diffusive limit, SIAM J. Numer. Anal., 35(6) (1998), 1073–1094.Google Scholar
[7] Larsen, A.W. and Morel, J.E., Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes. II, J. Comp. Phys., 83(1) (1989), 212–236.CrossRefGoogle Scholar
[8] Larsen, A.W., Morel, J.E. and Miller, W.F. Jr., Asymptotic solutions of numerical transport problems in optically thick, diffusiive regimes. J. Comput. Phys., 69(2) (1987), 283–324.Google Scholar
[9] Lee, C.E., The Discrete SN Approximation to Transport Theory, LA-2595, 1962.Google Scholar
[10] Mieussens, L., On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic model. J. Comput. Phys. 253 (2013), 138–156.Google Scholar
[11] van Leer, B., Towards the ultimate conservative difference schemes V. A second-order sequal to Godunov's method. J. Comput. Phys. 32 (1979), 101–136.Google Scholar
[12] Xu, K. and Huang, J.C., A unified gas-kinetic scheme for continuum and rarefied flows. J. Comput. Phys., 229 (2010), 7747–7764.Google Scholar
[13] Spitzer, L. and Harm, R., Transport phenomena in a completely ionized gas. Phys. Rev., 89 (1953), 977.Google Scholar
[14] Sun, W.J., Jiang, S., and Xu, K., An Asymptotic Preserving unified gas kinetic scheme for gray radiative transfer equations. J. Comput. Phys. 285 (2015), pp. 265–279.Google Scholar
[15] Sun, W.J., Jiang, S., Xu, K. and Li, S., An Asymptotic Preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations. J. Comput. Phys. 302 (2015), pp. 222–238.Google Scholar
[16] Mousseau, V.A. and Knoll, D.A., Temporal accuracy of the nonequilibrium radiation diffusion equations applied to two-dimensional multimaterial simulations. Nuclear Science and Engineering, 154 (2006), pp. 174–189.Google Scholar
[17] Chang, B., The incorporation of the semi-implicit linear equations into Newton's method to solve radiation transfer equations. J. Comput. Phys., 226 (2007), pp. 852–878.Google Scholar
[18] Larsen, E.W., A grey transport acceleration method for time-dependent radiative transfer problems. J. Comput. Phys. 78 (1988), pp. 459–480.Google Scholar
[19] Godillon-Lafitte, P. And Goudon, T., A Coupled Model For Radiative Transfer: Doppler Effects, Equilibrium, And Nonequilibrium Diffusion Asymptotics. Multiscale Model. Simul., 4(4) (2005), pp. 1245C1279.Google Scholar
[20] Bueta, C. and Despresa, B., Asymptotic analysis of (uid models for the coupling of radiation and hydrodynamics. Journal of Quantitative Spectroscopy and Radiative Transfer 85 (2004), PP. 385C418.Google Scholar