Shock propagation in a driven hard sphere gas: molecular dynamics simulations and hydrodynamics

TL;DR

This study investigates shock wave propagation in a driven hard sphere gas using molecular dynamics and hydrodynamic equations, revealing limitations of ideal models and the importance of dissipative effects for accurate descriptions.

Contribution

It compares molecular dynamics simulations with Euler and Navier-Stokes hydrodynamics, highlighting the need for dissipation to match observed shock behaviors.

Findings

Euler equations fail for localized driving with singularities.

Navier-Stokes equations with dissipation fit simulation data well.

Uniform driving leads to discrepancies between models and simulations.

Abstract

The continuous injection of energy in a stationary gas creates a shock wave that propagates radially outwards. We study the hydrodynamics of this disturbance using event driven molecular dynamics of a hard sphere gas in two and three dimensions, the numerical solution of the Euler equation with a virial equation of state for the gas, and the numerical solution of the Navier-Stokes equation, for the cases when the driving is localised in space and when it is uniform throughout the shock. We show that the results from the Euler equation do not agree with the data from hard sphere simulations when the driving is uniform and has singularities when the driving is localised. Including dissipative terms through the Navier-Stokes equation results in reasonably good description of the data, when the coefficients of dissipation are chose parametrically.