Steady-state shear flows via nonequilibrium molecular dynamics and smooth-particle applied mechanics

Abstract

We simulate both microscopic and macroscopic shear flows in two space dimensions using nonequilibrium molecular dynamics and smooth-particle applied mechanics. The time-reversible microscopic equations of motion are isomorphic to the smooth-particle description of inviscid macroscopic continuum mechanics. The corresponding microscopic particle interactions are relatively weak and long ranged. Though conventional Green-Kubo theory suggests instability or divergence in two-dimensional flows, we successfully define and measure a finite shear viscosity coefficient by simulating stationary plane Couette flow. The special nature of the weak long-ranged smooth-particle functions corresponds to an unusual kind of microscopic transport. This microscopic analog is mainly kinetic, even at high density. For the soft Lucy potential which we use in the present work, nearly all the system energy is potential, but the resulting shear viscosity is nearly all kinetic. We show that the measured shear viscosities can be understood, in terms of a simple weak-scattering model, and that this understanding is useful in assessing the usefulness of continuum simulations using the smooth-particle method. We apply that method to the Rayleigh-Bénard problem of thermally driven convection in a gravitational field.