A combined Event-Driven/Time-Driven molecular dynamics algorithm for the simulation of shock waves in rarefied gases

Abstract

A novel combined Event-Driven/Time-Driven (ED/TD) algorithm to speed-up the Molecular Dynamics simulation of rarefied gases using realistic spherically symmetric soft potentials is presented. Due to the low density regime, the proposed method correctly identifies the time that must elapse before the next interaction occurs, similarly to Event-Driven Molecular Dynamics. However, each interaction is treated using Time-Driven Molecular Dynamics, thereby integrating Newton’s Second Law using the sufficiently small time step needed to correctly resolve the atomic motion. Although infrequent, many-body interactions are also accounted for with a small approximation. The combined ED/TD method is shown to correctly reproduce translational relaxation in argon, described using the Lennard-Jones potential. For densities between ρ = 10 - 4 kg / m 3 and ρ = 10 - 1 kg / m 3 , comparisons with kinetic theory, Direct Simulation Monte Carlo, and pure Time-Driven Molecular Dynamics demonstrate that the ED/TD algorithm correctly reproduces the proper collision rates and the evolution toward thermal equilibrium. Finally, the combined ED/TD algorithm is applied to the simulation of a Mach 9 shock wave in rarefied argon. Density and temperature profiles as well as molecular velocity distributions accurately match DSMC results, and the shock thickness is within the experimental uncertainty. For the problems considered, the ED/TD algorithm ranged from several hundred to several thousand times faster than conventional Time-Driven MD. Moreover, the force calculation to integrate the molecular trajectories is found to contribute a negligible amount to the overall ED/TD simulation time. Therefore, this method could pave the way for the application of much more refined and expensive interatomic potentials, either classical or first-principles, to Molecular Dynamics simulations of shock waves in rarefied gases, involving vibrational nonequilibrium and chemical reactivity.