  An approach to derive low-complexity models describing thermal radiation for
the sake of simulating the behavior of electric arcs in switchgear systems is
presented. The idea is to approximate the (high dimensional) full-order
equations, modeling the propagation of the radiated intensity in space, with a
model of much lower dimension, whose parameters are identified by means of
nonlinear system identification techniques. The low-order model preserves the
main structural aspects of the full-order one, and its parameters can be
straightforwardly used in arc simulation tools based on computational fluid
dynamics. In particular, the model parameters can be used together with the
common approaches to resolve radiation in magnetohydrodynamic simulations,
including the discrete-ordinate method, the P-N methods and photohydrodynamics.
The proposed order reduction approach is able to systematically compute the
partitioning of the electromagnetic spectrum in frequency bands, and the
related absorption coefficients, that yield the best matching with respect to
the finely resolved absorption spectrum of the considered gaseous medium. It is
shown how the problem's structure can be exploited to improve the computational
efficiency when solving the resulting nonlinear optimization problem. In
addition to the order reduction approach and the related computational aspects,
an analysis by means of Laplace transform is presented, providing a
justification to the use of very low orders in the reduction procedure as
compared with the full-order model. Finally, comparisons between the full-order
model and the reduced-order ones are presented.
