In this chapter, we introduce homogeneous nonequilibrium molecular dynamics simulation techniques by discussing the theoretical background to the SLLOD equations of motion. When these equations of motion are used in conjunction with compatible periodic boundary conditions and a homogeneous thermostat, they provide a very robust, reliable and well-understood method for studying fluids subjected to homogeneous flows. Here, we introduce the SLLOD equations of motion for the simple case of atomic fluids. This provides the groundwork for our discussion of methods for simulating homogeneous flows of molecular fluids in Chapter 8.

The SLLOD Equations of Motion

Background

To conduct microscopic simulations of flows driven by boundaries, mimicking real physical systems (e.g. Couette or elongational flows) we must explicitly include the walls. This inevitably induces density inhomogeneities into the fluid. If one is interested in nano-confined flow, then this is an appropriate simulation strategy since spatial inhomogeneity needs to be explicitly included in the simulation. However, if one is concerned with computing bulk properties such as mass, momentum and heat transport coefficients that we do not want to be distorted by surface effects, then the explicit use of boundaries is inappropriate.

An alternative to using atomistic wall boundaries is to generate flow through a suitable implementation of periodic boundary conditions. The first and most popular method of inducing flow through the periodic boundary conditions employs the so called Lees-Edwards boundary conditions [15] to generate planar shear flow. In such a scheme, a simulation box is replicated in all directions by periodic images.