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Two-Stream Approximation to the radiative transfer equation:A New Improvement and Comparative Accuracy with Existing Methods

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Advances in Atmospheric Sciences 2024年第2期41卷 278-292页

作者： F.Momo TEMGOUA L.Akana NGUIMDO DNJOMO Environmental Energy Technologies Laboratory(EETL) Faculty of SciencesUniversity of YaoundéPO Box 812 YaoundéCameroon Department of Electrical and Electronic Engineering Faculty of Engineering and TechnologyUniversity of BueaPO Box 63 BueaCameroon

Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of app

关键词： radiative transfer equation two-stream method Legendre polynomial optical thickness moments of specific intensity conversion function transmittance reflectance

Temperature and Water Vapor Weighting Functions from radiative transfer equation with Surface Emissivity and Solar Reflectivity

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Advances in Atmospheric Sciences 1994年第4期11卷 421-426页

作者：李俊 Cooperative Institute for Meteorological Satellite Studies Space Science and Engineering Center University of Wisconsin-Madison. Madison WI 53706 U.S.A.

Linearization of radiative transfer equation (RTE) is the key step in physical retrieval of atmospheric temperature and moisture profiles from InfRared (IR) sounder observations. In this paper, the successive forms of temperature and water vapor mixing ratio component weighting functions are derived by applying one term variation method to RTE with surface emissivity and solar reflectivity contained. Retrivals of temperature and water vapor mixing ratio profiles from simulated Atmospheric Infrared Sounder (AIRS) observations with surface emissivity and solar reflectivity are presented.

关键词： radiative transfer equation Weighting Function Retrieval

Quantitative Evaluation of Bioluminescence Imaging Based on radiative transfer equation

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Chinese Journal of Biomedical Engineering(English Edition) 2016年第1期25卷 39-46页

作者： KAN Xing-xing CHEN Chun-xiao GONG Rong-fang Department of Biomedical Engineering Nanjing University of Aeronautics & Astronautics Department of Mathematics Nanjing University of Aeronautics & Astronautics

B iolum inescence in aghg is a khd ofem erghg detection technology at cellular, m olecu lar and genetic level. The most popular b io lum m inescence in aghg model is diffusion approxin ation （DA）. However, because of the ill-posedness of the D A -based hverse problem and the instability of reconstruction algorithm s, the location accuracy of the reconstucted sources is low. radiative transfer equation （RTE）, which considers the direction of the photon m igration and the effect of absorption and scattering in tissues, can accurately express the transmission ofbiolum hescent photns through the tissues. In this paper, we studied the biolum hescence inaging based on the RTE. 2D sinuiations were performed, and quantitative evaluation was given by the absolute source position error, the relative source area error and the m h in um bound hg box. The resu Its of the experin ent showed that the in aging quality based on R TE was beer than thatone based on D A.

关键词： biolum inescence in aghg radiative transfer equation disconthuous Galerkinmethod forward problem inverse problem

3D radiative transfer equation Coupled with Heat Conduction equation with Realistic Boundary Conditions Applied on Complex Geometries

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Journal of Applied Mathematics and Physics 2016年第8期4卷 1488-1493页

作者： D. Le Hardy Y. Favennec G. Domingues B. Rousseau Université de Nantes Nantes France

This paper presents the solution of coupled radiative transfer equation with heat conduction equation in complex three-dimensional geometries. Due to very different time scales for both physics, the radiative problem is considered steady-state but solved at each time iteration of the transient conduction problem. The discrete ordinate method along with the decentered streamline-upwind Petrov-Galerkin method is developed. Since specular reflection is considered on borders, a very accurate algorithm has been developed for calculation of partition ratio coefficients of incident solid angles to the several reflected solid angles. The developed algorithms are tested on a paraboloid-shaped geometry used for example on concentrated solar power technologies.

关键词： radiative transfer equation Heat Conduction equation Finite Element Methods SUPG DOM Specular Reflection Complex Geometry

Discrete Duality Finite Volume Discretization of the Thermal-P_(N) radiative transfer equations on General Meshes

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Communications in Computational Physics 2022年第2期31卷 398-448页

作者： Francois Hermeline Universite Paris-Saclay Laboratoire en Informatique Haute Performance pour le Calcul et la simulationCEADAMDIF91297 ArpajonFrance

The discrete duality finite volume method has proven to be a practical tool for discretizing partial differential equations coming from a wide variety of areas of physics on nearly arbitrary *** main ingredients of the method are:(1)use of three meshes,(2)use of the Gauss-Green theorem for the approximation of derivatives,(3)discrete integration by *** this article we propose to extend this method to the coupled grey thermal-P_(N) radiative transfer equations in Cartesian and cylindrical coordinates in order to be able to deal with two-dimensional Lagrangian approximations of the interaction of matter with *** stability under a Courant-Friedrichs-Lewy condition and the preservation of the diffusion asymptotic limit are proved while the experimental second-order accuracy is observed with manufactured *** numerical experiments are reported which show the good behavior of the method.

关键词： Hybrid multiscale models radiative transfer equation grey P_(N)approximation discrete duality finite volume method

The Radiation Loss of a Cylindrical Methane-Argon Plasma Arc

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Plasma Science and Technology 2010年第2期12卷 218-223页

作者： B.LIANI R.BENALLAL M.LEMERINI Theoretical Physics Laboratory Sciences Faculty University of Tlemcen

Calculation of the net radiation emitted by a CH4-Ar mixture, in a temperature range of 5,000-30,000 K with the assumption of local thermodynamic equilibrium （LTE）, is conducted. Continuum and line emissions are taken into account. The radiative transfer of each line is calculated by means of an escape factor depending on the shape and broadening of the line. Assuming a cylindrical, homogeneous, and isothermal plasma, the net emission coefficient is calculated for different pressures between 1 atm and 10 atm and arc radia of 0 mm to 1 mm. Results show that the argon presence in the CH4-Ar mixture has a significant effect on the total radiation emitted for the temperature above 17,000 K and the results for pure argon agree with those of BAUDER and EVANS.

关键词： thermal plasma methane argon radiation loss radiative transfer equation

辐射传输方程的变分和Galerkin离散格式

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高等学校计算数学学报 2018年第3期40卷 275-288页

作者：何莉敏王娟侯玉双内蒙古科技大学理学院西安交通大学数学与统计学院西南大学物理科学与技术学院

1引言辐射传输方程(radiative transfer equation:RTE)有着非常广泛的应用,例如天体物理[1],大气和海洋[2,3],辐射传热[4],中子输运[5,6],光分子成像[7,8]等等.辐射传输方程是光学分子成像的正向问题,从物理角度而言可归结为光子在生物... 详细信息

1引言辐射传输方程(radiative transfer equation:RTE)有着非常广泛的应用,例如天体物理[1],大气和海洋[2,3],辐射传热[4],中子输运[5,6],光分子成像[7,8]等等.辐射传输方程是光学分子成像的正向问题,从物理角度而言可归结为光子在生物组织中的传输问题,然而辐射传输方程是一个偏微分方程,本质上是一个积分-微分的双曲型问题,由于其自身问题的复杂性和高维性,目前寻找求解辐射传输方程的有效数值解法仍是一个严峻的

关键词： radiative transfer equation weak formulation variational principle exponential stability

A Free Streaming Contact Preserving Scheme for the M_(1) Model

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Advances in Applied Mathematics and Mechanics 2010年第3期2卷 259-285页

作者： C.Berthon J.Dubois B.Dubroca T.-H.Nguyen-Bui R.Turpault Universitéde Nantes Laboratoire de Mathématiques Jean Leray2 Rue de la Houssinière 44322 Nantes Cedex 3France CEA CESTA33114 Le BarpFrance UniversitéBordeaux I CELIA351 Cours de la libération33405 Talence CedexFrance

The present work concerns the numerical approximation of the M_(1) model for radiative *** main purpose is to introduce an accurate finite volume method according to the nonlinear system of conservation laws that governs this *** propose to derive an HLLC method which preserves the stationary contact *** supplement this essential property,the method is proved to be robust and to preserve the physical admissible ***,a relevant asymptotic preserving correction is proposed in order to obtain a method which is able to deal with all the physical *** relevance of the numerical procedure is exhibited thanks to numerical simulations of physical interest.

关键词： radiative transfer equation M_(1)model finite volume method Riemann solver HLLC scheme asymptotic preserving scheme

High-Precision Direct Method for the radiative transfer Problems

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Communications in Theoretical Physics 2013年第6期59卷 782-788页

作者： ZHANG Yan HOU Su-Qing YANG Ping WU Kai-Su Beijing University of Chemical Technology Beijing 100029 China Institute of Modern Physics Chinese Academy of Sciences Lanzhou 730000 China University of Chinese Academy of Sciences Beijing 100049 China

It is the main aim of this paper to investigate the numerical methods of the radiative transfer equation. Using the five-point formula to approximate the differential part and the Simpson formula to substitute for integral part respectively, a new high-precision numerical scheme, which has 4-order local truncation error, is obtained. Subsequently, a numerical example for radiative transfer equation is carried out, and the calculation results show that the new numerical scheme is more accurate.

关键词： radiative transfer equation direct method five-point numerical formula truncation error