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首页> 外文期刊>Journal of Quantitative Spectroscopy & Radiative Transfer >Finite element formulation of the first- and second-order discrete ordinates equations for radiative heat transfer calculation in three-dimensional participating media
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Finite element formulation of the first- and second-order discrete ordinates equations for radiative heat transfer calculation in three-dimensional participating media

机译：一维和二阶离散坐标方程在三维参与介质中辐射传热计算的有限元公式

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摘要

Two finite element methods (FEMs), FEDOM1 and FEDOM2 (standing for the first and the second finite element discrete ordinates methods, respectively), are formulated and numerically tested. The reference second-order discrete equation is modified in its scattering terms and is applied to the problems of absorbing/emitting and anisotropically scattering media by using the FEM. Numerical features of the developed FEMs are compared with one of the discrete ordinates interpolation method (DOIM), which uses a finite difference scheme. Prediction results of radiative heat transfer by these two FEMs are compared with reference solutions and verified in three-dimensional enclosures containing participating media. The results of FEDOM1 and FEDOM2 agree well with exact solutions for the problem of absorbing/emitting medium with various range of optical thickness. Generally, the two FEMs show more accurate results than DOIM. And FEDOM1 shows more accurate results than FEDOM2 in most of the test problems. Both of the developed FEMs show reasonable results compared with published Monte Carlo solutions for the tested absorbing/emitting and anisotropically scattering media. Although the FEDOM2 is not as accurate as the FEDOM1, it shows its own advantages that it reduces CPU time and memory space of dependent variable to half. (c) 2008 Elsevier Ltd. All rights reserved.
机译：制定并数值测试了两种有限元方法（FEM）：FEDOM1和FEDOM2（分别代表第一和第二个有限元离散坐标方法）。对参考二阶离散方程的散射项进行了修改，并通过有限元方法将其应用于吸收/发射和各向异性散射介质的问题。将已开发的有限元的数值特征与使用有限差分方案的离散坐标插值方法（DOIM）之一进行了比较。将这两个FEM产生的辐射热传递的预测结果与参考解决方案进行比较，并在包含参与介质的三维外壳中进行验证。 FEDOM1和FEDOM2的结果与吸收/发射具有各种光学厚度范围的介质的问题的精确解非常吻合。通常，这两个FEM显示出比DOIM更准确的结果。在大多数测试问题中，FEDOM1比FEDOM2显示更准确的结果。与已发布的蒙特卡洛解决方案相比，这两种已开发的FEM均显示出合理的结果，用于测试吸收/发射和各向异性散射介质。尽管FEDOM2不如FEDOM1准确，但它显示出自己的优势，即它将CPU时间和因变量的存储空间减少了一半。 （c）2008 Elsevier Ltd.保留所有权利。

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