Asymptotic preserving numerical schemes for a non-classical radiation transport model for atmospheric clouds

被引:9
作者
Krycki, Kai [1 ]
Berthon, Christophe [2 ]
Frank, Martin [1 ]
Turpault, Rodolphe [2 ]
机构
[1] Rhein Westfal TH Aachen, Ctr Computat Engn Sci, D-52062 Aachen, Germany
[2] Univ Nantes, Lab Math Jean Leray, F-44322 Nantes 03, France
关键词
Non-classical transport; radiative transfer; asymptotic preserving schemes; PARTICLE-TRANSPORT; BOLTZMANN-EQUATION; DIFFUSIVE REGIMES;
D O I
10.1002/mma.2733
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present numerical schemes for the P1-moment and M1-moment approximations of a non-classical transport equation modeling radiative transfer in atmospheric clouds. In contrast to classical radiative transfer, the photon path-length is introduced as an additional variable and serves as pseudo-time in this model. Because clouds may have optically thick regions, we introduce a diffusive scaling and show that the diffusion limits of the moment models and the original equations agree. Furthermore, we show that the numerical schemes also preserve the diffusion asymptotics as well as the set of admissible and realizable states, both for the explicit and the implicit discretization of the pseudo-time variable. A source iteration-like method is proposed, and we observe that it converges slowly in the optical thick case, but a suitable initialization can help to overcome this problem. We validate our method in 1D and present simulation results in the 2D-case for real cloud data. Copyright (c) 2013 John Wiley & Sons, Ltd.
引用
收藏
页码:2101 / 2116
页数:16
相关论文
共 21 条
[1]   Fast iterative methods for discrete-ordinates particle transport calculations [J].
Adams, ML ;
Larsen, EW .
PROGRESS IN NUCLEAR ENERGY, 2002, 40 (01) :3-159
[2]  
Aregba-Driollet D., 2012, ARXIV12076279V1
[3]   An HLLC scheme to solve the M1 model of radiative transfer in two space dimensions [J].
Berthon, Christophe ;
Charrier, Pierre ;
Dubroca, Bruno .
JOURNAL OF SCIENTIFIC COMPUTING, 2007, 31 (03) :347-389
[4]   An asymptotic preserving scheme for hydrodynamics radiative transfer models - Numerics for radiative transfer [J].
Buet, Christophe ;
Cordier, Stephane .
NUMERISCHE MATHEMATIK, 2007, 108 (02) :199-221
[5]   The 13RC -: Bringing together the most advanced radiative transfer tools for cloudy atmospheres [J].
Cahalan, RF ;
Oreopoulos, L ;
Marshak, A ;
Evans, KF ;
Davis, AB ;
Pincus, R ;
Yetzer, KH ;
Mayer, B ;
Davies, R ;
Ackerman, TP ;
Barker, HW ;
Clothiaux, EE ;
Ellingson, RG ;
Garay, MJ ;
Kassianov, E ;
Kinne, S ;
Macke, A ;
O'Hirok, W ;
Partain, PT ;
Prigarin, SM ;
Rublev, AN ;
Stephens, GL ;
Szczap, F ;
Takara, EE ;
Várnai, T ;
Wen, GY ;
Zhuravleva, TB .
BULLETIN OF THE AMERICAN METEOROLOGICAL SOCIETY, 2005, 86 (09) :1275-+
[6]   On the radiative equilibrium of a stellar atmosphere. II [J].
Chandrasekhar, S .
ASTROPHYSICAL JOURNAL, 1944, 100 (01) :76-86
[7]   Theoretical and numerical study on a moment closure hierarchy for the radiative transfer equation [J].
Dubroca, B ;
Feugeas, JL .
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 329 (10) :915-920
[8]   ON A GENERALIZED BOLTZMANN EQUATION FOR NON-CLASSICAL PARTICLE TRANSPORT [J].
Frank, Martin ;
Goudon, Thierry .
KINETIC AND RELATED MODELS, 2010, 3 (03) :395-407
[9]   Photon path length distributions for cloudy skies - oxygen A-band measurements and model calculations [J].
Funk, O ;
Pfeilsticker, K .
ANNALES GEOPHYSICAE, 2003, 21 (03) :615-626
[10]   The convergence of numerical transfer schemes in diffusive regimes I: Discrete-ordinate method [J].
Golse, F ;
Jin, S ;
Levermore, CD .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1999, 36 (05) :1333-1369