Dissipative particle dynamics at isothermal, isobaric, isoenergetic, and isoenthalpic conditions using Shardlow-like splitting algorithms.

Numerical integration schemes based upon the Shardlow-splitting algorithm (SSA) are presented for dissipative particle dynamics (DPD) approaches at various fixed conditions, including a constant-enthalpy (DPD-H) method that is developed by combining the equations-of-motion for a barostat with the equations-of-motion for the constant-energy (DPD-E) method. The DPD-H variant is developed for both a deterministic (Hoover) and stochastic (Langevin) barostat, where a barostat temperature is defined to satisfy the fluctuation-dissipation theorem for the Langevin barostat. For each variant, the Shardlow-splitting algorithm is formulated for both a velocity-Verlet scheme and an implicit scheme, where the velocity-Verlet scheme consistently performed better. The application of the Shardlow-splitting algorithm is particularly critical for the DPD-E and DPD-H variants, since it allows more temporally practical simulations to be carried out. The equivalence of the DPD variants is verified using both a standard DPD fluid model and a coarse-grain solid model. For both models, the DPD-E and DPD-H variants are further verified by instantaneously heating a slab of particles in the simulation cell, and subsequent monitoring of the evolution of the corresponding thermodynamic variables as the system approaches an equilibrated state while maintaining their respective constant-energy and constant-enthalpy conditions. The original SSA formulated for systems of equal-mass particles has been extended to systems of unequal-mass particles. The Fokker-Planck equation and derivations of the fluctuation-dissipation theorem for each DPD variant are also included for completeness.