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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.19786 |
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Table of Contents:
- For the water-air system, the bulk density ratio is as high as about 1000; no model can fully tackle such a high density ratio system. In the Navier-Stokes and Euler equations, the density $ρ$ within the water-air interface is assumed to be a constant based on the Boussinesq approximation namely $ρ(\mathrm{d} \mathbf u/\mathrm{d} t)$, which does not account for the true momentum evolution $\mathrm{d} (ρ\mathbf u)/\mathrm{d} t$ ($\mathbf u$-fluid velocity). Here, we present an alternative theory for the density evolution equations of immiscible fluids 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 provide a generalization of Bernoulli's principle for energy conservation and a general formulation for the sound speed. The present model can be applied for immiscible fluids with arbitrarily high density ratios, thereby, opening a new window for computational fluid dynamics both for compressible and incompressible fluids.