Dissipative particle dynamics with energy conservation: Isoenergetic integration and transport properties

Simulations of nano- to micro-meter scale fluidic systems under thermal gradients require consistent mesoscopic methods accounting for both hydrodynamic interactions and proper transport of energy. One such method is dissipative particle dynamics with energy conservation (DPDE), which has been used for various fluid systems with non-uniform temperature distributions. We propose an easily parallelizable modification of the velocity-Verlet algorithm based on local energy redistribution for each DPDE particle such that the total energy in a simulated system is conserved up to machine precision. Furthermore, transport properties of a DPDE fluid are analyzed in detail. In particular, an analytical approximation for the thermal conductivity coefficient is derived, which allows its a priori estimation for a given parameter set. Finally, we provide approximate expressions for the dimensionless Prandtl and Schmidt numbers, which characterize fluid transport properties and can be adjusted independently by a proper selection of model parameters. In conclusion, our results strengthen the DPDE method as a very robust approach for the investigation of mesoscopic systems with temperature inhomogeneities.