Self-consistent radiation based modelling of electric arcs: I. Efficient radiation approximations

We perform a systematic investigation of methods for including radiation transport in arc simulations by analysing both various ways of solving the radiation transfer equation and methods for averaging the absorption coefficient over frequency. We show that the discrete ordinate method (DOM) and the P(1) approximation can be used to produce good results: DOM being slightly more accurate and P(1) being faster. Furthermore, we demonstrate that it is possible to start from the full absorption spectrum and produce band-averaged absorption coefficients with sufficient accuracy, if the frequencies are grouped not only based on frequency but also based on their magnitude. This makes it possible to introduce radiation transport in arc simulations in a systematic manner, with full control of accuracy. In a follow-up paper, part II, we apply our results to the simulation of several switching arcs, demonstrating the feasibility of self-consistent arc simulations for switching applications.