本研究應用徑向函數 (radial basis function, RBF) 法展開以強度矩表示之輻射傳遞積分方程式中的強度矩，發展出一種無網格的解法，稱為 RBF-IEM。由於本方法不需要網格，較容易應用在不規則形狀的介質。本研究首先應用 RBF-IEM 於二維定折射及變折射係數矩形介質中的輻射傳遞問題，探討不同光學厚度，散射比及 RBF 中心點數對精確性的影響，結果顯示在光學厚度小時需要較多方向格點；光學厚度大時需要較多 RBF 中心點才能得到相同精確性。接著討論二維不規則幾何形狀介質，包括矩形缺角、半圓形內部挖孔介質的熱傳問題，針對不同散射比、折射率梯度及不同邊界性質時的結果進行討論，結果顯示不同散射比對 RBF-IEM 的精確度無明顯影響但不同折射率梯度對精確度則影響甚劇，而對於不規則形狀介質的輻射傳遞只要提供足夠多的方向格點，對本研究方法的精確度並不會影響太多，而當考慮的輻射傳遞問題邊界為反射邊界時，雖然需要多解一組積分方程式，計算時間仍然低於蒙地卡羅法 (Monte Carlo method, MCM)，並同時具有優異的精確度。

A radial basis function-based (RBF-based) meshless method is developed to solve the integral equations of radiative transfer in terms of intensity moments. Since the method does not require meshes, it can be readily applied to the problem with irregular geometry. The method is first applied to radiative transfer in a two-dimensional (2D) rectangular medium with a constant or varying refractive index to investigate the effects of different optical sizes, scattering albedos and RBF centres on the accuracy. The results obtained by using appropriate RBF centres show good accuracy. More RBF centres are required for optically thicker cases; more directional quadrature points are required for optically thinner cases. Radiative transfer in 2D irregular media, including a trapezoidal medium and a semicircular medium with a circle in it, is then studied. Various optical sizes, scattering albedos, gradients of refractive index and boundary properties are considered. The results show that the scattering albedo has little influence on accuracy while the gradient of refractive index affect accuracy greatly. The results also show that irregular geometry of medium does not degrade accuracy much, provided that the number of directional quadrature point is sufficiently large. As for the cases with reflecting surfaces, the computation cost of the present method is still less than that of the MCM, while the accuracy of the present results and that of the MCM are comparable.

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