Thermodynamic Theory of Incompressible Hydrodynamics

TL;DR

This paper develops a thermodynamic framework using the grand potential for incompressible fluid flows, deriving reduced equations from compressible Navier-Stokes and illustrating the approach with microflow simulations.

Contribution

It introduces a new thermodynamic formulation for incompressible hydrodynamics based on the grand potential, unifying models and numerical methods.

Findings

Derived reduced equations from compressible Navier-Stokes

Incompressible equations as quasi-stationary solutions

Simulation of microflow using minimal Boltzmann model

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.