On the numerical treatment of dissipative particle dynamics and related systems

TL;DR

This paper reviews and develops numerical methods for particle simulations that control temperature and preserve momentum, improving accuracy and efficiency in modeling complex fluids and polymers.

Contribution

It introduces a generalized pairwise thermostat scheme with feedback control and coupling with stochastic dynamics, enhancing ergodicity and computational efficiency.

Findings

Significant efficiency improvements up to 80% over existing methods.

Enhanced ergodicity with coupling of auxiliary variables and stochastic dynamics.

Development of splitting methods with high thermodynamic accuracy.

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 Nos\'{e}-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.