The spatial and angular domain decomposition method for radiation heat transfer in 2D rectangular enclosures with discontinuous boundary conditions

Abstract To remedy discontinuous boundary conditions, we propose the spatial and angular domain decomposition approach for the solution of radiative transfer equation (RTE) in a two-dimensional rectangular enclosure. The RTE is angularly and spatially discretized. For each spatial node, the total solid angle 4π is decomposed into several angular sub-domains according to the distribution of discontinuous boundaries, and the quadrature weighting factors are recalculated for each angular sub-domain by using the compound trapezoidal integral scheme. For each angularly-discretized direction, the spatial domain is decomposed into a few spatial sub-domains according to the distribution of discontinuous boundaries. In each spatial sub-domain the distribution of radiative intensity is continuous, and the angularly-discretized RTE is solved for each spatial sub-domain. Two examples are employed to verify the performance of the domain decomposition method, and the results confirm its suitability and advantage for treating radiative transfer problem with discontinuous boundary conditions.

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