From Molecular Dynamics to hydrodynamics - a novel Galilean invariant thermostat

Abstract

This article proposes a novel thermostat applicable to any particle-based dynamic simulation. Each pair of particles is thermostated either (with probability P) with a pairwise Lowe-Andersen thermostat, or (with probability 1-P) with a thermostat that is introduced here, which is based on a pairwise interaction similar to the Nose-Hoover thermostat. When the pairwise Nose-Hoover thermostat dominates (low P), the liquid has a high diffusion coefficient and low viscosity, but when the Lowe-Andersen thermostat dominates, the diffusion coefficient is low and viscosity is high. This novel Nose-Hoover-Lowe-Andersen thermostat is Galilean invariant and preserves both total linear and angular momentum of the system, due to the fact that the thermostatic forces between each pair of the particles are pairwise additive and central. We show by simulation that this thermostat also preserves hydrodynamics. For the (non-interacting) ideal gas at P=0, the diffusion coefficient diverges and viscosity is zero, while for P>0 it has a finite value. By adjusting probability P, the Schmidt number can be varied by orders of magnitude. The temperature deviation from the required value is at least an order of magnitude smaller than in Dissipative Particle Dynamics (DPD), while the equilibrium properties of the system are very well reproduced. Applications of this thermostat include all standard molecular dynamic simulations of dense liquids and solids with any type of force field, as well as hydrodynamic simulation of multi-phase systems with largely different bulk viscosities, including surface viscosity, and of dilute gases and plasmas.