Rankine-Hugoniot Relations for Lennard-Jones Liquids

Abstract

The purpose of the present study is to clarify the Rankine-Hugoniot relations for Lennard-Jones liquids. First, Monte Carlo simulations are conducted to evaluate the state quantities such as the pressures, the internal energies, and the sound velocities. These computed values are used to obtain the approximate expressions for the state quantities by the method of least squares. The Rankine-Hugoniot relations are then clarified numerically as a function of the shock Mach number by solving the basic equations together with those approximate expressions. For liquid shock waves, not only the pressure but also the temperature increases much larger than those for an ideal gas. The results obtained here enable us to conduct more efficient molecular dynamics simulations such as simulating shock fronts alone for the investigation of the internal structures of liquid shock waves.