Molecular dynamics simulations of normal shocks in dilute gases

Molecular Dynamics (MD) simulations, using the Lennard-Jones potential, are used to study the structure of normal shock waves in dilute argon. For moderate free stream densities (ρ1 = 1 kg/m³), large-scale parallel calculations are required to simulate the full shock flow. At very dilute conditions (ρ1 ∼ 10^-3 kg/m³), a combined Event-Driven/Time-Driven (ED/TD) algorithm is proposed to speed up the MD simulations using realistic spherically symmetric soft potentials. Because of the rarefied conditions, the novel combined scheme identifies the impending interaction (like in Event-Driven MD), however resolves each interaction adequately using Time-Driven MD with small time steps. This method correctly reproduces translational relaxation, and it is further validated by simulating full shock waves. Through detailed comparisons with Direct Simulation Monte Carlo (DSMC) solutions using the variable-hard-sphere (VHS) collision model, MD simulations allow a more sensitive evaluation of the VHS model parameters than possible using available experimental density data. Consistently with Chapman-Enskog theory, at high temperatures (300-8000 K), near-perfect agreement between MD and DSMC solutions is demonstrated and inverse shock thickness predictions reproduce experimental measurements. In the low temperature range (16-300 K), both theory and MD results show that the VHS collision model becomes less valid. At very dilute conditions, the ED/TD algorithm determines a significant speed-up, being up to several thousand times faster than conventional TD MD, depending on the problem. Therefore, with this method, it could be possible to use much more accurate and computationally demanding interatomic potentials, either classical or first principles, to include such physics as chemical reactivity and vibrational nonequilibrium.