  This work is concerned with the numerical simulation of plasma arc
interaction with aerospace substrates under conditions akin to lightning strike
and in particular with the accurate calculation of radiative heat losses. These
are important because they have a direct effect on the calculation of thermal
and pressure loads on the substrates, which can lead to material damage under
certain conditions. Direct numerical solution of the radiation transport
equation (RTE) in mesoscale simulations is not viable due to its computational
cost, so for practical applications reduced models are usually employed. To
this end, four approximations for solving the RTE are considered in this work,
ranging from a simple local thermodynamical behaviour consideration, to a more
complex spectral absorption dependent on the arc geometry. Their performance is
initially tested on a one-dimensional cylindrical arc, before implementing them
in a multi-dimensional magnetohydrodynamics code. Results indicate that
inclusion of spectral absorption is necessary in order to obtain consistent
results. However, the approaches accounting for the arc geometry require
repeated solution of the computationally intensive Helmholtz equations, making
them prohibitive for multi-dimensional simulations. As an alternative, a method
using the net emission coefficient is employed, which provides a balance
between computational efficiency and accuracy, as shown by comparisons against
experimental measurements for a plasma arc attaching to an aluminium substrate.
