  We reconsider some fundamental aspects of the fluid mechanics model, and the
derivation of continuum flow equations from gas kinetic theory. Two topologies
for fluid representation are presented, and a set of macroscopic equations are
derived through a modified version of the classical Boltzmann kinetic equation
for monatomic gases. The free volumes around the gaseous molecules are
introduced into the set of kinetic microscopic parameters. Our new description
comprises four, rather than three, conservation equations; the classical
continuity equation, which conflates actual mass-density and number-density in
a single equation, has been split into a conservation equation of mass (which
involves only the classical number-density of the gaseous particles) and an
evolution equation purely of the mass-density (mass divided by the actual
volume of the fluid). We propose this model as a better description of gas
flows displaying non-local-thermodynamic-equilibrium (rarefied flows), flows
with relatively large variations of macroscopic properties, and/or highly
compressible fluids/flows.
