A consistency study of coarse-grained dynamical chains through a Nonlinear wave equation of mixed type

Mingjie Liao, Ping Lin

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Abstract

A dynamical atomistic chain to simulate mechanical properties of a one-dimensional material with zero temperature may be modelled by the molecular dynamics (MD) model. Because the number of particles (atoms) is huge for a MD model, in practice one often takes a much smaller number of particles to formulate a coarsegrained approximation. We shall mainly consider the consistency of the coarse-grained model with respect to the grain (mesh) size to provide a justification to the goodness of such an approximation. In order to reduce the characteristic oscillations with very different frequencies in such a model, we either add a viscous term to the coarse-grained MD model or apply a space average to the coarse-grained MD solutions for the consistency study. The coarse-grained solution is also compared with the solution of the (macroscopic) continuum model (a nonlinear wave equation of mixed type) to show how well the coarse-grained model can approximate the macroscopic behavior of the material. We also briefly study the instability of the dynamical atomistic chain and the solution of the Riemann problem of the continuum model which may be related to the defect of the atomistic chain under a large deformation in certain locations.

Original languageEnglish
Pages (from-to)921-948
Number of pages28
JournalCommunications in Computational Physics
Volume27
Issue number3
Early online date2 Feb 2020
DOIs
Publication statusPublished - 2020

Keywords

  • Coarsegrained approximation
  • Conservation law
  • Instability
  • Mixed type wave equation
  • Riemann problems

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