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Applied Mathematics and Mechanics

, Volume 39, Issue 1, pp 63–82 | Cite as

A note on hydrodynamics from dissipative particle dynamics

  • X. BianEmail author
  • Z. Li
  • N. A. Adams
Article
  • 196 Downloads

Abstract

We calculate current correlation functions (CCFs) of dissipative particle dynamics (DPD) and compare them with results of molecular dynamics (MD) and solutions of linearized hydrodynamic equations. In particular, we consider three versions of DPD, the empirical/classical DPD, coarse-grained (CG) DPD with radial-direction interactions only and full (radial, transversal, and rotational) interactions between particles. To facilitate quantitative discussions, we consider specifically a star-polymer melt system at a moderate density. For bonded molecules, it is straightforward to define the CG variables and to further derive CG force fields for DPD within the framework of the Mori-Zwanzig formalism. For both transversal and longitudinal current correlation functions (TCCFs and LCCFs), we observe that results of MD, DPD, and hydrodynamic solutions agree with each other at the continuum limit. Below the continuum limit to certain length scales, results of MD deviate significantly from hydrodynamic solutions, whereas results of both empirical and CG DPD resemble those of MD. This indicates that the DPD method with Markovian force laws possibly has a larger applicability than the continuum description of a Newtonian fluid. This is worth being explored further to represent generalized hydrodynamics.

Key words

dissipative particle dynamics (DPD) fluctuating hydrodynamics molecular dynamics (MD) coarse-graining Mori-Zwanzig projection 

Chinese Library Classification

O352 

2010 Mathematics Subject Classification

82-08 82C31 76M28 

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Notes

Acknowledgements

Z. LI acknowledges funding support of the U. S. Army Research Laboratory with Cooperative Agreement No. W911NF-12-2-0023.

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chair of Aerodynamics and Fluid Mechanics, Department of Mechanical EngineeringTechnical University of MunichMünchenGermany
  2. 2.Division of Applied MathematicsBrown UniversityRhode IslandUSA

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