Abstract
This study puts emphasis on reducing the temperature error of dissipative particle dynamics (DPD) fluid by directly applying a minimal-stage third-order partitioned Runge-Kutta (PRK3) method to the time integration, which does not include any of additional governing equations and change in the DPD thermostat formulation. The error is estimated based on the average values of both kinetic and configurational temperatures. The result shows that the errors in both temperatures errors are greatly reduced by using the PRK3 scheme as comparing them to those of previous studies. Additionally, the comparison among three different PRK3 schemes demonstrates our recent findings that the symplecticity conservation of the system is important to reduce the temperature error of DPD fluid especially for large time increments. The computational efficiencies are also estimated for the PRK3 scheme as well as the existing ones. It was found from the estimation that the simulation using the PRK3 scheme is more than twice as efficient as those using the existing ones. Finally, the roles of both kinetic and configurational temperatures as error indicators are discussed by comparing them to the velocity autocorrelation function and the radial distribution function. It was found that the errors of these temperatures involve different characteristics, and thus both temperatures should be taken into account to comprehensively evaluate the numerical error of DPD.
Highlights
The importance of mesoscopic fluid simulations has been increasing to further investigate complex phenomena at this scale with minimal computational load
A set of simulations were implemented to compare the temperature errors estimated by using the PRK3 scheme to that by using the existing ones (M-Verlet, Shardlow, and M-Shardlow schemes), where an in-house computational code package were developed with Python and Fortran to perform these simulations
The set of random numbers ζ ij does not change within a time step in accordance with the characteristics of the Wiener process for all the time integration schemes
Summary
The importance of mesoscopic fluid simulations has been increasing to further investigate complex phenomena at this scale with minimal computational load. At this scale (approximately ranging between 10 nm and 10 μm), both hydrodynamics and thermal fluctuations are important, and a mesoscopic simulation method should be able to take into account these properties. Dissipative particle dynamics (DPD), which is a particle-based method first developed by Hoogerbrugge and Koleman [1], owns these properties and has been used for various simulations of mesoscopic complex fluid systems, such as colloidal suspensions [2,3], biological systems [4,5], and polymer solutions [6,7]. A number of recent researches have mainly focused on correctly handling the dissipative force to reduce the error by modifying time integration scheme such as the modified velocity-Verlet (M-Verlet) scheme [8], the scheme using the splitting technique [9]
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