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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >EXAMINATION OF SOLUTION METHODS FOR THE SECOND-ORDER DISCRETE ORDINATE FORMULATION
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EXAMINATION OF SOLUTION METHODS FOR THE SECOND-ORDER DISCRETE ORDINATE FORMULATION

机译：二阶离散正则公式的求解方法检验

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The radiative transfer equation is cast into a second-order formulation and various solution schemes are examined critically. The second-order formulation is valid for any type of scattering, and the numerical schemes are compatible with conventional control-volume grids. Number of ordinates is reduced to half when compared with the conventional (first-order) discrete ordinate method, while the resulting equation for the radiation transfer is a familiar second-order elliptic type. Methods of discretization and the numerical characteristics are discussed in depth. Three approaches to discretization are discussed: Taylor series, control-volume, and control-line approaches. The last method is considered most promising and is investigated in detail; i.e., two types of dependent variable evaluation along the line of sight are discussed-numerical differentiation and exact exponential schemes. Sample computation for a square enclosure with a cold black wad and gas of uniform temperature is made to check the characteristics such as false scattering, ray effect, etc. The control-line approach with a higher-order interpolation scheme gives better accuracy in general. Numerical differentiation along the line of sight gives the same result as the exact exponential schemes when the intergrid optical depth is small. However the latter is more accurate when the medium is optically thick. [References: 16]
机译：将辐射传递方程转化为二阶公式，并对各种解决方案进行严格审查。二阶公式适用于任何类型的散射，并且数值方案与常规控制体积网格兼容。与传统的（一阶）离散纵坐标方法相比，纵坐标的数量减少到一半，而辐射传输的结果方程式是熟悉的二阶椭圆类型。深入讨论了离散化方法和数值特征。讨论了离散化的三种方法：泰勒级数，控制量和控制线方法。最后一种方法被认为是最有前途的，并进行了详细研究。即，讨论了视线范围内的两种类型的因变量评估-数值微分和精确指数方案。对带有冷黑棉团和温度均匀的气体的方形外壳进行样本计算，以检查虚假散射，射线效应等特性。采用高阶插值方案的控制线方法通常可提供更好的精度。当网格光学深度较小时，沿视线的数值微分给出与精确指数方案相同的结果。但是，当介质光学上较厚时，后者更为准确。 [参考：16]

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