热辐射输运问题的隐式蒙特卡罗方法求解

热辐射与物质相互作用及辐射光子在物质中的传输是惯性约束聚变研究中的重要课题. 介绍了基于隐式蒙特卡罗方法的辐射输运方程,在该方程的积分-微分形式基础上,推导了利于蒙特卡罗方法模拟的等价的积分输运方程;基于积分方程设计数值模拟流程,编写三维蒙特卡罗数值模拟程序;针对热辐射输运典型问题及benchmark问题开展了数值实验,计算结果验证了方法的适应性及程序的正确性. 关键词： 热辐射 惯性约束聚变 输运方程 隐式蒙特卡罗     

Monte Carlo ray-tracing simulation for radiative heat transfer in turbulent fluctuating media under the optically thin fluctuation approximation

The Monte Carlo ray-tracing method (MCRT) based on the concept of radiation distribution factor is extended to solve radiative heat transfer problem in turbulent fluctuating media under the optically thin fluctuation approximation. A one-dimensional non-scattering turbulent fluctuating media is considered, in which the mean temperature and absorption coefficient distribution are assumed and the shape of probability density function is given. The distribution of the time-averaged volume radiation heat source is solved by MCRT and direct integration method. It is shown that the results of MCRT based on the concept of radiation distribution factor agree with these of integration solution very well, but results of MCRT based on the concept of radiative transfer coefficient do not agree with these of integration solution. The solution of time-averaged radiative transfer equation by the concept of radiative transfer coefficient should be treated with caution.     

Flux vector formulation for photon propagation in the biological tissue

We present a generalized delta-Eddington phase function to simplify the radiative transfer equation to an integral equation with respect to the photon flux vector. The solution of the integral equation is highly accurate to model the photon propagation in the biological tissue over a broad range of optical parameters, especially in the visible light spectrum where the diffusion approximation breaks down. The methodology is validated in the Monte Carlo simulation and can be applied in various optical imaging applications.     

Analysis of vector radiative transfer through a finite slab of a stochastic precipitation medium

The formulation and solution of the vector radiative transfer equation in a finite slab of a stochastic precipitation medium of binary rain rates are considered. The electromagnetic wave is supposed to encounter alternating layered segments of the two precipitation media, each with a deterministic rain rate. Both the backscattering coefficient and the bistatic coefficient are derived by taking an ensemble average of the iterative solution for the deterministic vector radiative transfer equation. Computer simulations are given to verify the solutions via the Monte Carlo method, to feature the distinctiveness of stochastic precipitation systems, and to illustrate the relationship between the stochastic parameters and the final results. It is also concluded from the computer simulations that a finite slab of a stochastic precipitation medium could be treated as an average rain-rate precipitation layer with an acceptable approximation.     

Comparing Diffusion Approximation with Radiation Transfer Analysis for Light Transport in Tissues

The diffusion model that is an approximation of the equation of radiation transfer is typically used to describe photon migration in scattering-dominant media. In general biological tissue is highly scattering and very weakly absorbing against near-infrared light, yet it is heterogeneous and may contain relatively highly absorbing or low-scattering regions. Here applicability of the diffusion approximation over the radiative transfer theory for describing ultrafast laser transport in biological tissues is numerically studied and investigated over different kinds of tissue conditions and geometries. Tissues having tumors of different sizes, locations and nature as well as dual-tumor and low-scattering conditions are considered. Radiation transfer analysis is taken as a comparison objective and it is initially proved to be accurate in benchmark comparisons with Monte Carlo simulation. The results predict systematically about the compatible conditions where and when we can use the diffusion approximation and the conditions in which the diffusion approximation may provide misleading results.     

CW laser transilluminance in turbid media with cylindrical inclusions

The present work analyzes the process of detection of small diffusive inclusions in turbid hosts. Experiments were carried out using a transillumination geometry and continuous wave laser radiation, considering cylindrical inclusions in different environments. A comparison between experimental data, theoretical approaches for the radiative transfer equation in the diffusion approximation, and numerical Monte Carlo simulations, is presented.     

Analytical solutions of the simplified spherical harmonics equations

We derived analytical solutions of the simplified spherical harmonics equations, an approximation of the radiative transfer equation, for infinitely extended scattering media. The derived equations are simple (sum of exponential functions) and quickly evaluated. We compared the solutions with Monte Carlo simulations in the steady-state and time domains and found much better agreement compared to solutions of the diffusion equation, especially for large absorption coefficients, short time values, and small distances from the source.     

A Monte Carlo method for 3D thermal infrared radiative transfer

A 3D Monte Carlo model for specific application to the broadband thermal radiative transfer has been developed in which the emissivities for gases and cloud particles are parameterized by using a single cubic element as the building block in 3D space. For spectral integration in the thermal infrared, the correlated k-distribution method has been used for the sorting of gaseous absorption lines in multiple-scattering atmospheres involving 3D clouds. To check the Monte-Carlo simulation, we compare a variety of 1D broadband atmospheric fluxes and heating rates to those computed from the conventional plane-parallel (PP) model and demonstrate excellent agreement between the two. Comparisons of the Monte Carlo results for broadband thermal cooling rates in 3D clouds to those computed from the delta-diffusion approximation for 3D radiative transfer and the independent pixel-by-pixel approximation are subsequently carried out to understand the relative merits of these approaches.     

Analytical approach for solving the radiative transfer equation in two-dimensional layered media

This study presents an analytical approach for obtaining Green's function of the two-dimensional radiative transfer equation to the boundary-value problem of a layered medium. A conventional Fourier transform and a modified Fourier series which is defined in a rotated reference frame are applied to derive an analytical solution of the radiance in the transformed space. The Monte Carlo method was used for a successful validation of the derived solutions.     

Asymptotic analysis of the spatial discretization of radiation absorption and re-emission in Implicit Monte Carlo

We perform an asymptotic analysis of the spatial discretization of radiation absorption and re-emission in Implicit Monte Carlo (IMC), a Monte Carlo technique for simulating nonlinear radiative transfer. Specifically, we examine the approximation of absorption and re-emission by a spatially continuous artificial-scattering process and either a piecewise-constant or piecewise-linear emission source within each spatial cell. We consider three asymptotic scalings representing (i) a time step that resolves the mean-free time, (ii) a Courant limit on the time-step size, and (iii) a fixed time step that does not depend on any asymptotic scaling. For the piecewise-constant approximation, we show that only the third scaling results in a valid discretization of the proper diffusion equation, which implies that IMC may generate inaccurate solutions with optically large spatial cells if time steps are refined. However, we also demonstrate that, for a certain class of problems, the piecewise-linear approximation yields an appropriate discretized diffusion equation under all three scalings. We therefore expect IMC to produce accurate solutions for a wider range of time-step sizes when the piecewise-linear instead of piecewise-constant discretization is employed. We demonstrate the validity of our analysis with a set of numerical examples.     

A hybrid transport-diffusion Monte Carlo method for frequency-dependent radiative-transfer simulations

Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations in optically thick media. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Each discrete step replaces many smaller Monte Carlo steps, thus improving the efficiency of the simulation. In this paper, we present an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold, as optical thickness is typically a decreasing function of frequency. Above this threshold we employ standard Monte Carlo, which results in a hybrid transport-diffusion scheme. With a set of frequency-dependent test problems, we confirm the accuracy and increased efficiency of our new DDMC method.     

Finite element approximation of the Fokker-Planck equation for diffuse optical tomography

In diffuse optical tomography, light transport theory is used to describe photon propagation inside turbid medium. A commonly used simplification for the radiative transport equation is the diffusion approximation due to computational feasibility. However, it is known that the diffusion approximation is not valid close to the sources and boundary and in low-scattering regions. Fokker-Planck equation describes light propagation when scattering is forward-peaked. In this article a numerical solution of the Fokker-Planck equation using finite element method is developed. Approach is validated against Monte Carlo simulation and compared with the diffusion approximation. The results show that the Fokker-Planck equation gives equal or better results than the diffusion approximation on the boundary of a homogeneous medium and in turbid medium containing a low-scattering region when scattering is forward-peaked.     

Approximate analytical solution to normal emittance of semi-transparent layer of an absorbing, scattering, and refracting medium

A two-step approximate analytical solution for the normal emittance of a plane layer of an absorbing, scattering and refracting medium is derived analytically. The analysis is based on the transport approximation and the two-step solution method for radiative transfer. The high accuracy of the approximate solution, examined by comparing its results to those obtained independently by the discrete ordinates and Monte Carlo methods, makes it suitable for application in combined experimental-analytical studies to identify selected spectral radiative properties of dispersed media in the range of semi-transparency.     

基于能量密度分布的辐射源粒子空间抽样方法研究

利用隐式蒙特卡罗方法模拟热辐射光子在物质中的输运过程时,物质辐射源粒子是需要细致处理的物理量.传统的物质辐射源粒子抽样方法是体平均抽样方法,对于大多数问题,这样处理不会带来大的偏差.但是对于一些辐射吸收截面大、单一网格内温差显著的问题,体平均抽样方法的计算结果偏差较大.分析了产生偏差原因,提出一种基于辐射能量密度分布的辐射源粒子空间位置抽样方法,并推导了相应的抽样公式以解决此类问题.数值实验表明,新方法计算结果明显优于原方法且与解析结果基本一致.     

热辐射输运问题的高效蒙特卡罗模拟方法

惯性约束聚变研究中,热辐射光子在介质中的输运以及热辐射光子与介质的相互作用是重要研究课题,蒙特卡罗方法是该类问题的重要研究手段之一.隐式蒙特卡罗方法虽然能正确地模拟热辐射在介质中的输运过程,但当模拟重介质(材料的吸收系数大)问题时,该方法花费的计算时间将变得很长,导致模拟效率很低.本文以离散扩散蒙特卡罗方法为基础,开发了"离散扩散蒙特卡罗方法辐射输运模拟程序",可以较好地解决重介质区的计算效率问题,但是离散扩散蒙卡罗方法在模拟轻介质区时精度不够高.辐射输运问题中通常既有轻介质也有重介质,为了能同时解决蒙特卡罗方法模拟的效率和精度问题,本文研究了离散扩散蒙特卡罗方法与隐式蒙特卡罗方法相结合的模拟方法,并提出了新的扩散区与输运区界面处理方法,研制了混合蒙特卡罗方法的辐射输运模拟程序.典型辐射输运问题模拟显示:在模拟重介质问题时,该程序能大幅缩短模拟时间,且能取得与隐式蒙特卡罗方法一致的结果;在模拟轻重介质均存在的问题时,与隐式蒙特卡罗方法相比,混合蒙特卡罗方法的模拟精度与其相当且计算效率同样能够得到显著提升.     

Monte Carlo discrete curved ray-tracing method for radiative transfer in an absorbing-emitting semitransparent slab with variable spatial refractive index

A Monte Carlo discrete curved ray-tracing method is developed to analyze the radiative transfer in one-dimensional absorbing-emitting semitransparent slab with variable spatial refractive index, in which the Monte Carlo method is combined with the discrete curved ray-tracing method. A problem of radiative equilibrium with linear variable spatial refractive index is taken as an example to examine the accuracy of the proposed method. The temperature distributions and the dimensionless radiative heat flux are determined by the proposed method and compared with the data in references, which are obtained by other different methods. The results show that the Monte Carlo discrete curved ray-tracing method has a good accuracy in solving the radiative transfer in one-dimensional semitransparent slab with variable spatial refractive index.     

A Monte Carlo implementation to solve radiation heat transfer in non-uniform media with spectrally dependent properties

This paper presents the application of the Monte Carlo method to solve the radiative heat exchange in non-homogeneous, non-isothermal gases with spectrally dependent properties. Among others models, the absorption-line blackbody (ALB) distribution function, originally defined and derived for the spectral line-based weighted-sum-of-gray-gases (SLW) model, allows an immediate, simple implementation of the Monte Carlo method to account the spectral dependence of the radiative properties. This work shows how the Monte Carlo method can be combined to the ALB distribution function, and provides results for heat transfer in a mixture of water vapor, carbon dioxide and nitrogen that have satisfactory agreement with the SLW method and with line-by-line integration. Finally, the solution technique is employed to solve two examples aiming at demonstrating the effect of the absorbing species concentration on the thermal radiative exchanges. The method is of great interest for the computation of radiative transfer in combustion systems where the chemical species concentration and the temperature are not uniform.     

太阳能吸热器玻璃窗辐射与导热计算

在太阳能塔式热发电空气吸热器工作过程中,吸热器玻璃窗受到聚焦太阳光、环境以及吸热面（体）的复合辐射。本文采用改进蒙特卡罗法、有限容积法,研究了太阳能空气吸热器石英玻璃窗半透明介质内部辐射与导热的耦合换热,研究了不同厚度半透明介质石英玻璃窗在工作面处于不同第三类边界条件下的稳态温度分布。研究表明石英玻璃的厚度和内侧空气温...