A two-dimensional nonlinear response matrix method with scattering and absorption-emission

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Abstract
A response matrix method is formulated for time-independent multi-dimensional, grey radiative transfer problems in which both scattering and absorption-emission are present and which are nonlinear as a result of temperature-dependent heat sources. The method is in sharp contrast to iterative techniques in which each iteration consists of a computation of the radiation intensity over the entire space-angle domain before the temperature field is updated. The nonlinear response matrix approach is unique in that within each spatial cell the temperature and outgoing radiation intensity are calculated in response only to the incoming radiation intensity. The updating of the temperature distribution therefore is placed within the iterative solution for the radiation intensity, rather than being placed outside of it. The method is implemented using the diamond-differenced discrete ordinate approximation and incorporated into one and two-dimensional computer codes utilizing standard red-black solution algorithms. Results are obtained for a number of problems both with fixed sources and with highly temperature-dependent combustion sources, the latter being characteristic of coal suspensions. Unaccelerated comparisons with standard discrete ordinate solution algorithms indicate improved efficiency to result from the response matrix method provided the spatial mesh is sufficiently coarse.

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