Blast waves in two and three dimensions: Euler versus Navier Stokes equations

TL;DR

This paper demonstrates that incorporating heat conduction and viscosity via the Navier Stokes equations resolves discrepancies between classical Euler solutions and molecular dynamics simulations of blast waves in two and three dimensions.

Contribution

It shows that the Navier Stokes equations, including heat conduction and viscosity, are necessary for accurate modeling of blast waves, improving upon the classical Euler solutions.

Findings

Euler solutions do not match molecular dynamics results.

Navier Stokes equations with heat conduction and viscosity align with simulations.

Including dissipative effects is essential for accurate blast wave modeling.

Abstract

The exact solution of the Euler equation, which describes the time evolution of a blast wave created by an intense explosion, is a classic problem in gas dynamics. However, it has been found that the analytical results do not match with results from molecular dynamics simulation of hard spheres in two and three dimensions. In this paper, we show that the mismatch between theory and simulations can be resolved by considering the Navier Stokes equation. From the direct numerical simulation of the Navier Stokes equation in two and three dimensions, we show that the inclusion of heat conduction and viscosity terms is essential to capture the results from molecular dynamics simulations.