Prediction of radiative intensity on thermal radiation transfer with graded index media by element differential method

The element differential method (EDM) is developed to solve the radiative transfer equation in graded index media, which can obtain high angular and spatial resolutions of radiative intensity. To discretize the angular domain, the discrete ordinates method (DOM) is adopted, and the element differential method is also adopted to discretize the spatial domain. Meanwhile, due to the radiative transfer equation's strong convection character-istics, an upwind scheme is used to suppress non-physical oscillations. Several examples of thermal radiation transfer in the two-dimensional geometry are chosen to test the capability of this model. Compared with the results in the references, the model has higher accuracy and efficiency in graded index media. The radiative intensity in three-dimensional angular distribution is further displayed. It can be proved that the upwind scheme can actively suppress non-physical oscillation and achieve stable calculation. Besides, the element differential method can also deal with radiation discontinuities. In conclusion, the results can provide a reference for thermal radiation analysis in graded index media.

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This paper presents the element differential method (EDM) for solving the radiative transfer equation in graded index media, achieving high angular and spatial resolutions of radiative intensity. The angular domain is discretized using the discrete ordinates method (DOM), while the spatial domain is discretized using the element differential method. An upwind scheme is employed to suppress non-physical oscillations due to the strong convection characteristics of the radiative transfer equation. Several examples demonstrate the model's higher accuracy and efficiency compared to existing references in graded index media. The results also show that the upwind scheme effectively suppresses non-physical oscillations and the element differential method handles radiation discontinuities.