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中国电机工程学报 2007, 27(32) 105-110 DOI:
ISSN: 0258-8013 CN: 11-2107/TM |
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梯度折射率介质内二阶辐射传递方程及其有限元求解 |
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张琳 刘林华 |
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哈尔滨工业大学能源科学与工程学院 哈尔滨工业大学能源科学与工程学院 |
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摘要：
梯度折射率介质内的辐射传递方程可以看作是一类特殊的对流型方程，对流项的存在能够引起解的非物理振荡。该文给出了一个梯度折射率介质离散坐标形式的二阶方程，同时发展了基于此离散坐标形式二阶方程的有限元法用于求解多维半透明梯度折射率介质内的辐射传递问题，最后通过5个算例进行验证。结果表明，与一阶梯度折射率介质辐射传递方程相比，二阶方程具有更好的数值特性，可以有效消除强对流特性引起的非物理振荡现象。基于二阶方程的有限元法可以精确且稳定地求解多维半透明梯度折射率介质内的辐射传递。 |
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关键词：
辐射传递
梯度折射率
半透明介质
有限元法
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Second Order Radiative Transfer Equation in Graded Index Medium and Its Solution by Finite Element Method |
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Abstract:
The equation of radiative transfer in graded index medium can be taken as a special kind of convection-dominated equation. The presence of convection term may cause nonphysical oscillation of numerical solutions. A second order differential form of the discrete ordinates equation of radiative transfer in graded index medium (SOGRTE) was derived and a finite element method based on the SOGRTE (SOGRTE-FEM) was developed. The SOGRTE- FEM was verified and its performances were studied by five test problems. It is shown that the SOGRTE has better numerical properties as compared to the original first order radiative transfer equation and can effectively bate nonphysical oscillation of solutions caused by strong convection character- ristics. The SOGRTE-FEM is stable and accurate to solve radiative transfer in multidimensional graded index medium. |
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Keywords:
radiative heat transfer
graded index
semitransparent medium
finite element simulation
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收稿日期 2007-03-23 修回日期 1900-01-01 网络版发布日期 |
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DOI: |
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基金项目:
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通讯作者: 刘林华 |
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作者简介: |
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作者Email: lhliu@hit.edu.cn |
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| 参考文献： |
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