  This study contributes to the body of work on instabilities in the
homogeneous cooling system focusing on clustering in the multiphase
gas-particle system. The critical system size for the onset of instability,
$L^*_c$, is studied via three different numerical methods: i) particle resolved
direct numerical simulation; ii) computational fluid dynamics-discrete element
method; and iii) a two-fluid model derived from kinetic theory. In general, the
$L^*_c$ results at several concentrations, inelasticities and initial thermal
Reynolds numbers are in good qualitative agreement with one another.
Additionally, most of the expected trends (i.e., general $L^*_c (\phi)$
behavior) are observed. However, there is a larger level of quantitative
discrepancy between the continuum and discrete particle methods than observed
previous (simpler) granular results. While the level of agreement may be
expected to decrease with the increased physical complexity of the gas-solid
system, a significant time-dependence is revealed and shown to be responsible
for some of the oddities in the numerical data.
