Higher-Order Finite Elements for Computing Thermal Radiation

Two variants of the finite-element method have been developed for use in computational simulations of radiative transfers of heat among diffuse gray surfaces. Both variants involve the use of higher-order finite elements, across which temperatures and radiative quantities are assumed to vary according to certain approximations. In this and other applications, higherorder finite elements are used to increase (relative to classical finite elements, which are assumed to be isothermal) the accuracies of final numerical results without having to refine computational meshes excessively and thereby incur excessive computation times.One of the variants is termed the radiation sub-element (RSE) method, which, itself, is subject to a number of variations. This is the simplest and most straightforward approach to representation of spatially variable surface radiation. Any computer code that, heretofore, could model surface-to-surface radiation can incorporate the RSE method without major modifications.