半透明介质中辐射传热的解析与数值研究
Analytical and numerical investigation of radiative heat transfer in semitransparent Media
AI总结：
本文研究辐射积分传热方程的数学和数值特性，证明了解的存在性和唯一性，并通过边界元方法验证了方法的有效性和准确性。
摘要：
本文致力于研究辐射积分传热方程的数学和数值特性。首先，分析了辐射积分算子的性质。基于这些结果，通过算子矩阵的可逆性证明了辐射积分系统的解的存在性和唯一性。此外，还进行了迭代方案的收敛性分析。然后，基于插值方案的边界元方法被用于离散辐射积分系统。考虑了任意封闭几何形状。对于非凸几何形状，开发了元素细分算法来处理包含可见因子的积分。最后，通过实例验证了该方法的有效性和准确性。
英文摘要：
This paper is devoted to deal with some mathematical and numerical aspects of the radiative integral transfer equations. First, the properties of the raidative integral operators are analyzed. Based on these results, the existence and uniqueness of solution to the radiative integral system is proved by the reversibility of operator matrix. Besides, the convergence analysis of an iterative scheme is also carried out. Then, boundary element method based on the collocation scheme is used to discretize the radiative integral system. Arbitrary enclosure geometry is considered. For the non-convex geometries, an element-subdivision algorithm is developed to handle with the integrals contained the visibility factor. Finally, examples are presented to verify the effectiveness and accuracy of our method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
