Stable schemes for dissipative particle dynamics with conserved energy

TL;DR

This paper introduces a novel numerical scheme for dissipative particle dynamics with conserved energy, utilizing a Metropolis-Hastings approach to enhance stability and allow larger timesteps in simulations.

Contribution

The proposed scheme reduces pairwise stochastic dynamics to single-variable dynamics and applies Metropolis-Hastings to prevent negative energies, improving simulation stability and efficiency.

Findings

No negative internal energies during simulation

Allows larger timesteps for systems with small heat capacities

Stability limited only by Hamiltonian dynamics

Abstract

This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal conduction) to effective single-variable dynamics, and to approximate the solution of these dynamics with one step of a Metropolis-Hastings algorithm. This ensures by construction that no negative internal energies are encountered during the simulation, and hence allows to increase the admissible timesteps to integrate the dynamics, even for systems with small heat capacities. Stability is only limited by the Hamiltonian part of the dynamics, which suggests resorting to multiple timestep strategies where the stochastic part is integrated less frequently than the Hamiltonian one.