  We present an update to the framework called SImulator of GAlaxy
Millimeter/submillimeter Emission (S\'IGAME). S\'IGAME derives line emission in
the far-infrared (FIR) for galaxies in particle-based cosmological
hydrodynamics simulations by applying radiative transfer and physics recipes
via a post-processing step after completion of the simulation. In this version,
a new technique is developed to model higher gas densities by parametrizing the
gas density probability distribution function (PDF) in higher resolution
simulations for use as a look-up table, allowing for more adaptive PDFs than in
previous work. S\'IGAME v3 is tested on redshift z = 0 galaxies drawn from the
SIMBA cosmological simulation for eight FIR emission lines tracing vastly
different interstellar medium phases. Including dust radiative transfer with
SKIRT and high resolution photo-ionization models with Cloudy, this new method
is able to self-consistently reproduce observed relations between line
luminosity and star formation rate in all cases, except for [NII]122, [NII]205
and [OI]63, the luminosities of which are overestimated by median factors of
1.6, 1.2 and 1.2 dex, respectively. We attribute the remaining disagreement
with observations to the lack of precise attenuation of the interstellar light
on subgrid scales (<200 pc).
