  The calculation of internal atmospheric (longwave) fluxes is a key component
of any model of exoplanet atmospheres that requires radiative-transfer (RT)
calculations. For atmospheres containing a strong scattering component such as
cloud particles, most 1D multiple-scattering RT methods typically involve
numerically expensive matrix inversions. This computational bottleneck is
exacerbated when multitudes of RT calculations are required, such as in general
circulation models (GCMs) and retrieval methods. In an effort to increase the
speed of RT calculations without sacrificing too much accuracy, we investigate
the applicability of approximate longwave scattering methods developed for the
Earth science community to hot Jupiter atmospheres. We test the absorption
approximation (AA) and variational iteration method (VIM) applied to typical
cloudy hot Jupiter scenarios, using 64 stream DISORT calculations as reference
solutions. We find the four-stream VIM variant is a highly promising method to
explore using for hot Jupiter GCM and retrieval modelling, showing excellent
speed characteristics, with typical errors $\sim$1\% for outgoing fluxes and
within $\sim$50\%, but with larger errors in the deep cloud layer test case,
for vertical heating rates. Other methods explored in this study were found to
typically produce similar error characteristics in vertical heating rates.
