  Astrophysical observations originate from matter that interacts with
radiation or transported particles. We develop a pragmatic approximation in
order to enable multi-dimensional simulations with basic spectral radiative
transfer when the computational resources are not sufficient to solve the
complete Boltzmann transport equation. The distribution function of the
transported particles is decomposed into trapped and streaming particle
components. Their separate evolution equations are coupled by a source term
that converts trapped particles into streaming particles. We determine this
source term by requiring the correct diffusion limit. For a smooth transition
to the free streaming regime, this 'diffusion source' is limited by the matter
emissivity. The resulting streaming particle emission rates are integrated over
space to obtain the streaming particle flux. A geometric estimate of the flux
factor is used to convert the particle flux to the streaming particle density.
The efficiency of the scheme results from the freedom to use different
approximations for each particle component. In supernovae, reactions with
trapped particles on fast time scales establish equilibria that reduce the
number of primitive variables required to evolve the trapped particle
component. On the other hand, a stationary-state approximation facilitates the
treatment of the streaming particle component. Different approximations may
apply in applications to stellar atmospheres, star formation, or cosmological
radiative transfer. We compare the isotropic diffusion source approximation
with Boltzmann neutrino transport of electron flavour neutrinos in spherically
symmetric supernova models and find good agreement. An extension of the scheme
to the multi-dimensional case is also discussed.
