  For the water-air system, the density ratio is as high as about 1000; no
model can fully tackle such a high density ratio system. Here, we present an
alternative theory for the density evolution equations in computational fluid
dynamics, differing from the concept of Navier-Stokes and Euler equations. Our
derivation is built upon the physical principle of energy minimization from the
aspect of thermodynamics. The present results are consistent with Landau's
theory of sound speed, and, most importantly, provide a generalization of
Bernoulli's principle for energy conservation. The present model can be applied
for immiscible fluids with arbitrary density ratios, thereby, opening a new
window for computational fluid dynamics both for compressible and
incompressible fluids.
