  We consider three conservative forms of the mildly compressible Euler
equations, called CE1, CE2 and CE3, with the goal of understanding which leads
to the most accurate and robust pressure-based solver in a finite volume
environment. Forms CE1 and CE2 are both written in density, momentum, and
specific enthalpy, but employ two different treatments of the buoyancy and
pressure gradient terms: for CE1 it is the standard pressure splitting
implemented in open-source finite volume solvers (e.g., OpenFOAM), while for
CE2 it is the typical pressure splitting found in computational atmospheric
studies. Form CE3 is written in density, momentum, and potential temperature,
with the buoyancy and pressure terms addressed as in CE2. For each formulation,
we adopt a computationally efficient splitting approach. The three formulations
are thoroughly assessed and compared through six benchmark tests involving dry
air flow over a flat terrain or orography. We found that all three models are
able to provide accurate results for the tests with a flat terrain, although
the solvers based on the CE2 and CE3 forms are more robust. As for the mountain
tests, CE1 solutions become unstable, while the CE2 and CE3 models provide
results in very good agreement with data in the literature, the CE3 model being
the most accurate. Hence, the CE3 model is the most accurate, reliable, and
robust for the simulation of mesoscale atmospheric flows when using a
pressure-based approach and space discretization by a finite volume method.
