A History of constitutive modeling via molecular dynamics: Shock waves in fluids and gases

Abstract

From its inception in the mid-Fifties, the method of molecular-dynamics (MD) computer simulations has been used to probe the foundations of statistical mechanics, first for equilibrium equation-of-state averages, and then for transport properties from equilibrium fluctuations. Traditional statistical mechanical theoreticians were shocked to see that this new-fangled computational physics approach was feasible, even with incredibly tiny samples (on the order of a hundred atoms). When direct measurement of transport coefficients by non-equilibrium molecular dynamics (NEMD) was proposed in the early Seventies, even greater resistance was encountered from the traditionalists – though evidence for convergence with the equilibrium fluctuation method gradually accumulated. In the late Seventies and early Eighties, shock-wave simulations by NEMD made it possible to test directly the principal continuum constitutive theory for fluids, namely, Navier-Stokes viscous flow and Fourier’s Law of heat conduction. To everyone’s surprise – and the consternation of many – NEMD, once again, demonstrated that continuum theory applies at embarrassingly small (atomistic) time and length scales. We pursue this early line of work into the modern era, showing how NEMD shock-wave simulations can still provide surprising insights and improvements upon our understanding of constitutive modeling.