A Nonlinear Moment Model for Radiative Transfer Equation

Formal Solutions for Polarized Radiative Transfer. II. High-order Methods

When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial grids. Aiming to provide a clear comparison between formal solvers, this work presents different high-order numerical schemes and applies the systematic analysis proposed by Janett et al. (2017), emphasizing their advantages and drawbacks in terms of order of accuracy, stability, and computational cost.

Monte Carlo simulations in anomalous radiative transfer: a tutorial

Anomalous radiative transfer (ART) theory is a generalization of classical radiative transfer theory. The present tutorial wants to show how Monte Carlo (MC) codes describing photons transport in anomalous media can be implemented. It is shown that the heart of the method consists in suitably describing, in a "non-classical" manner, photons steps starting from fixed light sources or from boundaries separating regions of the medium with different optical properties. To give a better intuition of the importance of these particular photon step lengths, it is also shown numerically that the descri…

高超声速大气进入中辐射传递与材料烧蚀响应相互作用的数值研究

Numerical Investigation of Radiative Transfers Interactions with Material Ablative Response for Hypersonic Atmospheric Entry

本研究提出高保真紧耦合多求解器框架，准确捕捉高超声速流动中辐射传递与材料烧蚀的相互作用，揭示烧蚀产物对辐射热通量的吸收与发射特性，强调紧耦合方法的必要性。

Continuum approach based on radiation distribution function for radiative heat transfer in densely packed particulate system

The study of radiative heat transfer in particulate system is usually based on radiative transfer equation (RTE) with effective radiative properties. However, for non-random, densely and regularly packed particulate systems, the applicability of RTE is questionable due to dependent scattering and weak randomness of particle arrangement. In this paper, a new continuum approach that does not explicitly rely on the RTE is proposed for radiative heat transfer in the densely packed particulate system. The new approach is based on the generalization of the concept of radiation distribution factor (R…

Asymptotic $P_N$ Approximation in Radiative Transfer Problems

We study the validity of the time-dependent asymptotic $P_N$ approximation in radiative transfer of photons. The time-dependent asymptotic $P_N$ is an approximation which uses the standard $P_N$ equations with a closure that is based on the asymptotic solution of the exact Boltzmann equation for a homogeneous problem, in space and time. The asymptotic $P_N$ approximation for radiative transfer requires careful treatment regarding the closure equation. Specifically, the mean number of particles that are emitted per collision ($ω_{\mathrm{eff}}$) can be larger than one due to inner or outer radi…

最小二乘有限元法求解强非均匀介质中辐射转移的一个不足问题

A Deficiency Problem of the Least Squares Finite Element Method for Solving Radiative Transfer in Strongly Inhomogeneous Media

采用频域方法对最小二乘有限元法（LSFEM）和伽辽金有限元法（GFEM）求解均匀和非均匀介质中辐射转移的精度和稳定性进行了理论研究。理论结果证实了传统的理解，优越的稳定性LSFEM相比，GFEM。然而，数值模拟和理论分析表明，LSFEM在求解强非均匀介质中的辐射转移时存在不足。LSFEM的这一缺陷将导致其精度严重下降，从而使LSFEM的性能大打折扣，使其不适合求解强非均匀介质中的辐射转移问题。从理论上证明了LSFEM与中心差分格式离散的二阶形式的辐射转移方程是等价的。

辐射输运方程的量子算法

Quantum Algorithm for Radiative Transfer Equation

本研究结合晶格玻尔兹曼方法提出一种覆盖辐射输运全核心物理过程的量子算法，相较经典算法可指数级加速计算，经IBM Qiskit Aer模拟验证结果与精确解吻合，为容错量子计算机拓展多领域应用。