Turbulence via intermolecular potential: A weakly compressible model of gas flow at low Mach number

TL;DR

This paper introduces a weakly compressible turbulence model for inertial gas flow at low Mach numbers, improving the realism of density and temperature behavior while maintaining turbulence development.

Contribution

It proposes a new pressure treatment that balances compressible and incompressible flow characteristics, enabling more realistic simulations of turbulent gas flow.

Findings

Turbulence develops similarly to inertial flow in the new model.

Density and temperature behave more realistically in the weakly compressible model.

The pressure equation damps divergence without enforcing incompressibility.

Abstract

In our recent works we proposed a theory of turbulence in inertial gas flow via the mean field effect of an intermolecular potential. We found that, in inertial flow, turbulence indeed spontaneously develops from a laminar initial condition, just as observed in nature and experiments. However, we also found that density and temperature in our inertial flow model behave unrealistically. The goal of the current work is to demonstrate technical possibility of modeling compressible, turbulent flow at low Mach number where both density and temperature behave in a more realistic fashion. Here we focus on a new treatment of the pressure variable, which constitutes a compromise between compressible, incompressible and inertial flow. Similarly to incompressible flow, the proposed equation for the pressure variable is artificial, rather than derived directly from kinetic formulation. However, unlike that for incompressible flow, our pressure equation only damps the divergence of velocity, instead of setting it directly to zero. We find that turbulence develops in our weakly compressible model much like it does in the inertial flow model, but density and temperature behave more realistically.