Microscopic origin of self-similarity in granular blast waves

TL;DR

This paper investigates the microscopic mechanisms behind self-similar blast wave expansion in granular media, combining simulations and continuum models to understand their unique scaling, profiles, and instabilities, especially at higher densities.

Contribution

It provides a detailed analysis linking molecular dynamics and hydrodynamics to explain self-similarity in granular blasts, including new insights into energy conservation and the breakdown of classical solutions.

Findings

Hydrodynamic profiles and scaling properties are accurately predicted by combined microscopic and continuum methods.

The classic TvNS solution breaks down at higher densities in granular media.

Instability of the self-similar solution is characterized and analyzed.

Abstract

The self-similar expansion of a blast wave, well-studied in air, has peculiar counterparts in dense and dissipative media such as granular gases. Recent results have shown that, while the traditional Taylor-von Neumann-Sedov (TvNS) derivation is not applicable to such granular blasts, they can nevertheless be well understood via a combination of microscopic and hydrodynamic insights. In this article, we provide a detailed analysis of these methods associating Molecular Dynamics simulations and continuum equations, which successfully predict hydrodynamic profiles, scaling properties and the instability of the self-similar solution. We also present new results for the energy conserving case, including the particle-level analysis of the classic TvNS solution and its breakdown at higher densities.