Molecular Dynamics Simulation of Compressible Fluid Flow in Two-Dimensional Channels

TL;DR

This paper presents a novel molecular dynamics simulation method to analyze compressible fluid flow in two-dimensional channels, revealing detailed velocity, temperature, and density distributions and proposing an equation for density distribution.

Contribution

The study introduces an efficient, dynamically layered data structure for molecular dynamics simulations of compressible flow in channels, providing new insights into flow properties at high Mach numbers.

Findings

Velocity distribution is nearly quadratic across the channel.

Temperature distribution is approximately quartic across the channel.

Density distribution is non-uniform and matches predictions from compressibility arguments.

Abstract

We study compressible fluid flow in narrow two-dimensional channels using a novel molecular dynamics simulation method. In the simulation area, an upstream source is maintained at constant density and temperature while a downstream reservoir is kept at vacuum. The channel is sufficiently long in the direction of the flow that the finite length has little effect on the properties of the fluid in the central region. The simulated system is represented by an efficient data structure, whose internal elements are created and manipulated dynamically in a layered fashion. Consequently the code is highly efficient and manifests completely linear performance in simulations of large systems. We obtain the steady-state velocity, temperature, and density distributions in the system. The velocity distribution across the channel is very nearly a quadratic function of the distance from the center of the channel and reveals velocity slip at the boundaries; the temperature distribution is only approximately a quartic function of this distance from the center to the channel. The density distribution across the channel is non-uniform. We attribute this non-uniformity to the relatively high Mach number, approximately 0.5, in the fluid flow. An equation for the density distribution based on simple compressibility arguments is proposed; its predictions agree well with the simulation results. Validity of the concept of local dynamic temperature and the variation of the temperature along the channel are discussed.