Solution of the radiative transfer equation in discrete ordinate form by sequential function approximation

Abstract An adaptive and scalable alternative to the finite element and finite volume methods is developed to solve the steady multi-dimensional radiative transport equation. Solutions to the problem of heat transfer within a two-dimensional box through a non–scattering medium are presented and compared to the results from popular finite volume methods. The accuracy level of the developed method, using skewed piecewise linear bases, surpasses that of the finite volume results using the popular step and diamond schemes on a regular grid. Moreover, the accuracy levels are achieved with less than 1 % of the number of control volumes used by the finite volume methods.

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