Foundations of dissipative particle dynamics

We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. This procedure links the forces between the dissipative particles to a hydrodynamic description of the underlying molecular dynamics (MD) particles. In particular, the dissipative particle forces are given directly in terms of the viscosity emergent from MD, while the interparticle energy transfer is similarly given by the heat conductivity derived from MD. In linking the microscopic and mesoscopic descriptions we thus rely on the macroscopic or phenomenological description emergent from MD. Thus the rules governing this form of dissipative particle dynamics reflect the underlying molecular dynamics; in particular, all the underlying conservation laws carry over from the microscopic to the mesoscopic description. We obtain the forces experienced by the dissipative particles together with an approximate form of the associated equilibrium distribution. Whereas previously the dissipative particles were spheres of fixed size and mass, now they are defined as cells on a Voronoi lattice with variable masses and sizes. This Voronoi lattice arises naturally from the coarse-graining procedure, which may be applied iteratively and thus represents a form of renormalization-group mapping. It enables us to select any desired local scale for the mesoscopic description of a given problem. Indeed, the method may be used to deal with situations in which several different length scales are simultaneously present. We compare and contrast this particulate model with existing continuum fluid dynamics techniques, which rely on a purely macroscopic and phenomenological approach. Simulations carried out with the present scheme show good agreement with theoretical predictions for the equilibrium behavior.