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Transient hydrodynamic finite-size effects in simulations under periodic boundary conditions

Adelchi J. Asta, Maximilien Levesque, Rodolphe Vuilleumier, and Benjamin Rotenberg
Phys. Rev. E 95, 061301(R) – Published 20 June 2017

Abstract

We use lattice-Boltzmann and analytical calculations to investigate transient hydrodynamic finite-size effects induced by the use of periodic boundary conditions. These effects are inevitable in simulations at the molecular, mesoscopic, or continuum levels of description. We analyze the transient response to a local perturbation in the fluid and obtain the local velocity correlation function via linear response theory. This approach is validated by comparing the finite-size effects on the steady-state velocity with the known results for the diffusion coefficient. We next investigate the full time dependence of the local velocity autocorrelation function. We find at long times a crossover between the expected t3/2 hydrodynamic tail and an oscillatory exponential decay, and study the scaling with the system size of the crossover time, exponential rate and amplitude, and oscillation frequency. We interpret these results from the analytic solution of the compressible Navier-Stokes equation for the slowest modes, which are set by the system size. The present work not only provides a comprehensive analysis of hydrodynamic finite-size effects in bulk fluids, which arise regardless of the level of description and simulation algorithm, but also establishes the lattice-Boltzmann method as a suitable tool to investigate such effects in general.

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  • Received 4 February 2017

DOI:https://doi.org/10.1103/PhysRevE.95.061301

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsPolymers & Soft Matter

Authors & Affiliations

Adelchi J. Asta1, Maximilien Levesque2,3, Rodolphe Vuilleumier2,3, and Benjamin Rotenberg1,4

  • 1Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 8234 PHENIX, 4 Place Jussieu, 75005 Paris, France
  • 2Ecole Normale Supérieure, PSL Research University, UPMC Univ Paris 06, CNRS, Département de Chimie, PASTEUR, 24 rue Lhomond, 75005 Paris, France
  • 3Sorbonne Universités, UPMC Univ Paris 06, ENS, CNRS, PASTEUR, 75005 Paris, France
  • 4Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, France

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Issue

Vol. 95, Iss. 6 — June 2017

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