Spectral Method For One-Dimensional Radiative Transfer Equation

Many numerical methods have been developed for solving radiative heat transfer problems in semitransparent media, such as, zonal method, heat flux method, Monte-Carlo method, and discrete ordinates method, etc. By comprehensive comparison, the methods based on discretization of the differential form of radiative transfer equation possess very good flexibility. However, there are still some disadvantages existing in the former methods. It is necessary to develop a high accurate, efficient and simple numerical method to solve radiative transfer equations.Spectral methods can somewhat overcome the drawbacks of low order methods, and can provide accurate results, while their solution procedures of spectral methods are something efficient and simple. The author develops and studies the characteristics of spectral methods to solve radiative transfer equation in semitransparent media. The present research contains two parts:1. The spectral method is used to solve radiative transfer equation in one-dimensional Cartesian coordinate systems. The numerical stability of spectral methods is investigated for solving radiative heat transfer under the both cases of non-scattering media and scattering media. The present numerical solutions are compared with those of references by exact or other numerical methods. The results show that the spectral methods have good accuracy and efficiency for solving one-dimensional radiative heat transfer problems.2. Spectral methods are presented to solve radiative heat transfer equations and coupled conduction-radiation problems in spherical media. An error comparison is made between present results and those from references. The final conclusions can be obtained that:the spectral methods can be used to solve radiative heat transfer alone, and can also to solve the coupled conduction-radiation problems in one-dimensional spherical media system efficiently.