Shock propagation following an intense explosion: comparison between hydrodynamics and simulations

TL;DR

This study compares classical hydrodynamic predictions of blast wave propagation with detailed molecular dynamics simulations, revealing discrepancies due to non-equilibrium effects and assumptions in the theory.

Contribution

It critically evaluates hydrodynamic theory against microscopic simulations and highlights the limitations of local equilibrium assumptions in modeling blast waves.

Findings

Hydrodynamic predictions do not match simulation data well.

Replacing ideal gas law with virial equation improves predictions.

Velocity fluctuations show non-Gaussian tails, indicating non-equilibrium.

Abstract

The solution for the radial distribution of pressure, density, temperature and flow velocity fields in a blast wave propagating through a medium at rest, following an intense explosion, starting from hydrodynamic equations, is one of the classic problems in gas dynamics. However, there is very little direct verification of the theory and its assumptions from simulations of microscopic models. In this paper, we compare the results and assumptions of the hydrodynamic theory with results from large scale event driven molecular dynamics simulations of a hard sphere gas in three dimensions. We find that the predictions for the radial distribution of the thermodynamic quantities do not match well with the numerical data. We improve the theory by replacing the ideal gas law with a more realistic virial equation of state for the hard sphere gas. While this improves the theoretical predictions, we show that they still fail to describe the data well. To understand the reasons for this discrepancy, the different assumptions of the hydrodynamic theory are tested within the simulations. A key assumption of the theory is the existence of a local equation of state. We validate this assumption by showing that the local pressure, temperature and density obey the equation of state for a hard sphere gas. However, the probability distribution of the velocity fluctuations has non-gaussian tails, especially away from the shock front, showing that the assumption of local equilibrium is violated. This, along with neglect of heat conduction, could be the possible reasons for the mismatch between theory and simulations.