Abstract
We review and compare numerical methods that simultaneously control temperature while preserving the momentum, a family of particle simulation methods commonly used for the modelling of complex fluids and polymers. The class of methods considered includes dissipative particle dynamics (DPD) as well as extended stochastic-dynamics models incorporating a generalized pairwise thermostat scheme in which stochastic forces are eliminated and the coefficient of dissipation is treated as an additional auxiliary variable subject to a feedback (kinetic energy) control mechanism. In the latter case, we consider the addition of a coupling of the auxiliary variable, as in the Nosé–Hoover–Langevin (NHL) method, with stochastic dynamics to ensure ergodicity, and find that the convergence of ensemble averages is substantially improved. To this end, splitting methods are developed and studied in terms of their thermodynamic accuracy, two-point correlation functions, and convergence. In terms of computational efficiency as measured by the ratio of thermodynamic accuracy to CPU time, we report significant advantages in simulation for the pairwise NHL method compared to popular alternative schemes (up to an 80% improvement), without degradation of convergence rate. The momentum-conserving thermostat technique described here provides a consistent hydrodynamic model in the low-friction regime, but it will also be of use in both equilibrium and nonequilibrium molecular simulation applications owing to its efficiency and simple numerical implementation.
Highlights
Stochastic momentum-conserving thermostats, which correctly capture long-ranged hydrodynamic interactions, are increasingly popular tools for simulation of simple and complex fluids [1]
As in the pairwise Nosé–Hoover (PNH) thermostat, the pairwise Nosé–Hoover–Langevin (PNHL) thermostat has the potential of being useful in nonequilibrium molecular dynamics (NEMD), but we focus on the application of dissipative particle dynamics (DPD) in this article
According to the black dashed second order line in the figure, all the methods seem to have second order convergence to the invariant measure, which verifies the error analysis results on nonsymmetric DPD-S1, LA and Peters thermostats in Section 4, but is a bit surprising for DPD-VV, NHLA, PNH and PNHL-N methods that were based on nonsymmetric splittings
Summary
Stochastic momentum-conserving thermostats, which correctly capture long-ranged hydrodynamic interactions, are increasingly popular tools for simulation of simple and complex fluids [1]. The first important scheme of this type was dissipative particle dynamics (DPD), introduced by Hoogerbrugge and Koelman [2] in 1992 for simulating complex hydrodynamic behavior at a mesoscopic level that is not accessible by conventional molecular dynamics (MD) [3,4]. In DPD, a collection of fluid molecules are grouped at the coarse-grained level and treated as a discrete particle. These particles interact at short range in a soft potential, thereby allowing larger timesteps than would be possible in MD, while simultaneously decreasing the number of degrees of freedom required. Shang / Journal of Computational Physics 280 (2015) 72–95 recover thermodynamic, dynamical and rheological properties of complex fluids, with applications to colloidal particles [5], polymer molecules [6] and fluid mixtures [7]
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