Application of a field-based method to spatially varying thermal transport problems in molecular dynamics

This paper derives a methodology to enable spatial and temporal control of thermally inhomogeneous molecular dynamics (MD) simulations. The primary goal is to perform non-equilibrium MD of thermal transport analogous to continuum solutions of heat flow which have complex initial and boundary conditions, moving MD beyond quasi-equilibrium simulations using periodic boundary conditions. In our paradigm, the entire spatial domain is filled with atoms and overlaid with a finite element (FE) mesh. The representation of continuous variables on this mesh allows fixed temperature and fixed heat flux boundary conditions to be applied, non-equilibrium initial conditions to be imposed and source terms to be added to the atomistic system. In effect, the FE mesh defines a large length scale over which atomic quantities can be locally averaged to derive continuous fields. Unlike coupling methods which require a surrogate model of thermal transport like Fourier's law, in this work the FE grid is only employed for its projection, averaging and interpolation properties. Inherent in this approach is the assumption that MD observables of interest, e.g. temperature, can be mapped to a continuous representation in a non-equilibrium setting. This assumption is taken advantage of to derive a single, unified set of control forces based on Gaussian isokinetic thermostats to regulate the temperature and heat flux locally in the MD. Example problems are used to illustrate potential applications. In addition to the physical results, data relevant to understanding the numerical effects of the method on these systems are also presented