On the numerical treatment of dissipative particle dynamics and related systems

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.

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Cited by in corpus (16)

• Perspective: Dissipative Particle Dynamics
• On the effect of the thermostat in non-equilibrium molecular dynamics simulations
• Adaptive Thermostats for Noisy Gradient Systems
• Structure-preserving integrators for dissipative systems based on reversible-irreversible splitting
• Pairwise adaptive thermostats for improved accuracy and stability in dissipative particle dynamics
• Assessing numerical methods for molecular and particle simulation
• On the connection between dissipative particle dynamics and the Itô-Stratonovich dilemma
• Stable schemes for dissipative particle dynamics with conserved energy
• Accurate and robust splitting methods for the generalized Langevin equation with a positive Prony series memory kernel
• New parallelizable schemes for integrating the Dissipative Particle Dynamics with Energy Conservation
• Time correlation functions of equilibrium and nonequilibrium Langevin dynamics: Derivations and numerics using random numbers
• The strong convergence of operator-splitting methods for the Langevin dynamics model
• Accurate and efficient splitting methods for dissipative particle dynamics
• Dissipative particle dynamics with energy conservation: isoenergetic integration and transport properties
• A stochastic Hamiltonian formulation applied to dissipative particle dynamics
• Stochastic Norton dynamics: An alternative approach for the computation of transport coefficients in dissipative particle dynamics