Theory and simulation of shock waves freely propagating through monoatomic non-Boltzmann gas

TL;DR

This paper investigates how non-Boltzmann energy distributions affect shock wave propagation in monoatomic gases through theoretical derivation and molecular dynamics simulations, revealing slower shock speeds and altered wave dynamics.

Contribution

It derives a non-Boltzmann heat capacity ratio from first principles and validates its effects on shock wave behavior via simulations, extending classical shock theory.

Findings

Shock wave propagates about 9% slower in non-Boltzmann gases.

Contact wave appears about 4% faster in non-Boltzmann gases.

The observed effects align with classical shock equations using the derived heat capacity ratio.

Abstract

The effect of non-Boltzmann energy distributions on the free propagation of shock waves through a monoatomic gas is investigated via theory and simulation. First, the non-Boltzmann heat capacity ratio $\gamma$, as a key property for describing shock waves, is derived from first principles via microcanonical integration. Second, atomistic molecular dynamics simulations resembling a shock tube setup are used to test the theory. The presented theory provides heat capacity ratios ranging from the well-known $\gamma = 5/3$ for Boltzmann energy-distributed gas to $\gamma \to 1$ for delta energy-distributed gas. The molecular dynamics simulations of Boltzmann and non-Boltzmann driven gases suggest that the shock wave propagates about 9% slower through the non-Boltzmann driven gas, while the contact wave appears to be about 4% faster if it trails non-Boltzmann driven gas. The observed slowdown of the shock wave through applying a non-Boltzmann energy distribution was found to be consistent with the classical shock wave equations when applying the non-Boltzmann heat capacity ratio. These fundamental findings provide novel insights into the behavior of non-Boltzmann gases and might help to improve the understanding of gas dynamical phenomena.