  The purpose of this work is to introduce a novel POD-Galerkin strategy for
the hybrid finite volume/finite element solver introduced in Berm\'udez et al.
2014 and Busto et al. 2018. The interest is into the incompressible
Navier-Stokes equations coupled with an additional transport equation. The full
order model employed in this article makes use of staggered meshes. This
feature will be conveyed to the reduced order model leading to the definition
of reduced basis spaces in both meshes. The reduced order model presented
herein accounts for velocity, pressure, and a transport-related variable. The
pressure term at both the full order and the reduced order level is
reconstructed making use of a projection method. More precisely, a Poisson
equation for pressure is considered within the reduced order model. Results are
verified against three-dimensional manufactured test cases. Moreover a modified
version of the classical cavity test benchmark including the transport of a
species is analysed.
