Shock propagation in the hard sphere gas in two dimensions: comparison between simulations and hydrodynamics

TL;DR

This study compares molecular dynamics simulations with hydrodynamic models for shock wave propagation in a two-dimensional hard sphere gas, revealing discrepancies similar to those found in three dimensions and questioning hydrodynamics' applicability.

Contribution

The paper provides large-scale simulations in two dimensions showing hydrodynamics fails to accurately predict shock propagation, highlighting limitations of hydrodynamic assumptions.

Findings

Hydrodynamics does not match simulation data well in 2D.

Discrepancies are similar to those observed in 3D cases.

Hydrodynamic assumptions like local equilibrium are challenged.

Abstract

We study the radial distribution of pressure, density, temperature and flow velocity fields at different times in a two dimensional hard sphere gas that is initially at rest and disturbed by injecting kinetic energy in a localized region through large scale event driven molecular dynamics simulations. For large times, the growth of these distributions are scale invariant. The hydrodynamic description of the problem, obtained from the continuity equations for the three conserved quantities -- mass, momentum, and energy -- is identical to those used to describe the hydrodynamic regime of a blast wave propagating through a medium at rest, following an intense explosion, a classic problem in gas dynamics. Earlier work showed that the results from simulations matched well with the predictions from hydrodynamics in two dimensions, but did not match well in three dimensions. To resolve this contradiction, we perform large scale simulations in two dimensions, and show that like in three dimensions, hydrodynamics does not describe the simulation data well. To account for this discrepancy, we check in our simulations the different assumptions of the hydrodynamic approach like local equilibrium, existence of an equation of state, neglect of heat conduction and viscosity.