OUR RECENT WORKS ON THE COLLOCATION SPECTRAL METHOD FOR THERMAL RADIATION IN PARTICIPATING MEDIA

Abstract

Due to the motivation of numerical simulation on radiative magnetohydrodynamics, as the first step, in recent few years, the authors and co-workers have adopted Chebyshev collocation spectral method (CSM) for the solutions of radiation transfer equation (RTE) in different situations and obtained many achievements. The solution cases include 1D thermal radiation with strong fluctuations and complex boundary conditions, coupled radiation and conduction in concentric spherical participating medium, pure radiation in graded index media, the steady and transient combination of radiation and conduction, etc. One most valuable work is the direct 3D Schurdecomposition for the 3D matrix equations after the discretization of RTE. The process of the applications of collocation spectral method to thermal radiation is introduced beginning from 3D case. The most favourite parts of CSM for RTE are the direct solution, the very high spatial accuracy, and the good potential of incorporation into computational fluid dynamics (CFD) and magnetohydrodynamics (MHD). As to irregular multi-dimensional geometric systems, CSM can also be adopted to solve the RTE together with the body fitted coordinates (BFC). Compared with discrete ordinates method (DOM), the accuracy of CSM is more sensitive to the number of discretized directions. Some obstacles, say, the direct solution of RTE under the cases of nonhomogeneous radiative properties, the inconsistence between the spectral accuracy in space and the only second-order accuracy in angular discretization, are stated. Finally, some possible futures are mentioned. NOMENCLATURE , , A B C coefficient square matrices in Eq. (5) p c specific heat (Jkg K)