Abstract
Radiative intensity with high directional and spatial resolutions can provide abundant useful information for combustion diagnosis systems based on radiative images. In this paper, an angular-spatial upwind element differential method (ASUEDM) is developed to discretize angular direction and spatial domain of radiative transfer equation (RTE) in a spherically participating medium. Because of the strong convection characteristic of radiative transfer equation, an upwind scheme is adopted to suppress the numerical oscillation. Meanwhile, Chebyshev-Gauss-Lobatto nodes are used to minimize the effect of the Runge phenomenon. Unlike conductive or convective boundary conditions, radiative boundary condition is unidirectional boundary condition, and a singularity node exists at the boundary. To deal with this singularity, we propose a discontinuous strategy. Three examples of radiative heat transfer in concentric spheres are chosen to test the capability of ASUEDM. Compared with benchmark solutions, ASUEDM can provide higher accuracy than discrete ordinates method or finite volume method. Besides, ASUEDM can flexibly provide hp convergence rate and achieve high-resolution characterization in angular direction and spatial domain.
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