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中文摘要：
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。
英文摘要：
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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Spectral Element Approach for Coupled Radiative and Conductive Heat Transfer in Semitransparent Medi
Discontinuous Finite Element Method for Radiative Heat Transfer in Semitransparent Graded Index Medi
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Verification of Numerical Simulation Method for Entropy Generation of Radiation Heat Transfer in Sem
Discontinuous Spectral Element Approach for Solving Radiative Heat Transfer in Multidimensional Semi
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