Unité de Recherche de Mécanique et de Modélisation des Systèmes Physiques (UR2MSP), Department of Physics, University of Dschang, Cameroon.
School of Energy and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China.
Phys Rev E. 2023 Jan;107(1-2):015302. doi: 10.1103/PhysRevE.107.015302.
The lattice Boltzmann method (LBM) has been developed as a powerful solution method in computational fluid dynamics and heat transfer. However, the development of the LBM for solving radiative transfer problems has been far from perfect. This paper proposes a generalized form of the lattice Boltzmann model for the multidimensional radiative transfer equation (RTE) in irregular geometry with a graded index based on body-fitted coordinates. The macroscopic RTE is recovered from Chapman-Enskog analysis, which provides two possible procedures to formulate the Boltzmann equation in graded-index media and irregular geometries. These proposed models have been tested by considering one-and two-dimensional problems of the RTE, and the benchmark solutions reported in the literature were used for comparisons. Afterwards, the LBM is used to analyze the radiation transport in graded-index media for various forms of scattering law, refractive index, boundary reflection, laser and optical properties, and temperatures. The graded-index function and the geometry type have a significant effect on radiative transport in cases in which the refractive index matches or mismatches the boundary. It is also apparent that the developed LBM is an efficient, powerful, robust, and accurate solver for radiative transport in inhomogeneous media with a graded-index function and irregular geometries.
格子玻尔兹曼方法（LBM）已发展成为计算流体动力学和传热学中的一种强大的求解方法。然而，用于解决辐射传递问题的 LBM 的发展还远不完善。本文提出了一种基于贴体坐标系的具有梯度折射率的多维辐射传递方程（RTE）的广义格子玻尔兹曼模型。宏观 RTE 可以通过 Chapman-Enskog 分析恢复，这为在梯度折射率介质和不规则几何形状中构建玻尔兹曼方程提供了两种可能的方法。通过考虑 RTE 的一维和二维问题来测试所提出的模型，并使用文献中报告的基准解决方案进行比较。之后，使用 LBM 分析各种散射律、折射率、边界反射、激光和光学特性以及温度下梯度折射率介质中的辐射传输。在折射率与边界匹配或不匹配的情况下，梯度折射率函数和几何形状对辐射传输有显著影响。显然，所开发的 LBM 是一种高效、强大、鲁棒和精确的求解器，可用于具有梯度折射率函数和不规则几何形状的非均匀介质中的辐射传输。
