Thermodynamic Theory of Incompressible Hydrodynamics

Abstract

The grand potential for open systems describes thermodynamics of fluid flows at low Mach numbers. A new system of reduced equations for the grand potential and the fluid momentum is derived from the compressible Navier-Stokes equations. The incompressible Navier-Stokes equations are the quasi-stationary solution to the new system. It is argued that the grand canonical ensemble is the unifying concept for the derivation of models and numerical methods for incompressible fluids, illustrated here with a simulation of a minimal Boltzmann model in a microflow setup.

4 pages, 1 figure, final version, accepted for publication in Physical Review Letters

References in corpus (2)

• Minimal entropic kinetic models for simulating hydrodynamics
• Kinetic Theory of Turbulence Modeling: Smallness Parameter, Scaling and Microscopic Derivation of Smagorinsky Model

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• General and exact pressure evolution equation
• A moving-grid approach for fluid-structure interaction problems with hybrid lattice Boltzmann method
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• Entropically damped artificial compressibility for the discretization corrected particle strength exchange method in incompressible fluid mechanics
• A general pressure equation based method for incompressible two-phase flows
• Reduced kinetic model of polyatomic gases
• Development of a Weakly Compressible Solver for Incompressible Two-Phase Flows
• Numerical simulation of two-phase incompressible viscous flows using general pressure equation
• Modeling gasodynamic vortex cooling