Shock propagation following an intense explosion in an inhomogeneous gas: core scaling and hydrodynamics

TL;DR

This paper investigates shock wave behavior in inhomogeneous gases after explosions, highlighting the limitations of Euler equations and the effectiveness of Navier-Stokes equations in capturing core dynamics through simulations.

Contribution

It generalizes the exact solution of Euler equations for inhomogeneous gases and demonstrates the necessity of Navier-Stokes equations for accurate core behavior modeling.

Findings

Euler equations fail near shock center for general initial conditions.

Navier-Stokes equations accurately describe shock core dynamics.

Derived and confirmed the crossover length scale for dissipation effects.

Abstract

We study the shock propagation in a spatially inhomogeneous gas following an intense explosion. We generalize the exact solution of the Euler equation for the spatio-temporal variation of density, velocity, and temperature to arbitrary dimensions. From the asymptotic behavior of the solution near the shock center, we argue that only for a critical dimension dependent initial density distribution will the Euler equation provide a correct description of the problem. For general initial density distributions, we use event-driven molecular dynamics simulations in one dimension to demonstrate that the Euler equation fails to capture the behavior near the shock center. However, the Navier-Stokes equation successfully resolves this issue. The crossover length scale below which the dissipation terms are relevant and the core scaling for the data near the shock center are derived and confirmed in EDMD simulations.