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

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 \(\gamma \rightarrow 1\) 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 insights into the behavior of non-Boltzmann gases and might help to improve the understanding of gas dynamical phenomena.