A Consistency Study of Coarse-Grained Dynamical Chains through a Nonlinear Wave Equation of Mixed Type (Communications in Computational Physics, 2020)
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 coarse-grained approximation. We shall mainly consider the consistency of the coarse-grainedmodel with respect to the grain (mesh) size to provide a justification to the goodness ofsuch 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-grainedMD 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 showhow well the coarse-grained model can approximate the macroscopic behavior of thematerial. We also briefly study the instability of the dynamical atomistic chain and thesolution of the Riemann problem of the continuum model which may be related to thedefect of the atomistic chain under a large deformation in certain locations.