A continuum–atomistic multi-scale analysis of temperature field problems and its application in phononic nano-structures

Abstract

In this paper, a novel coupling technique is developed in continuum–atomistic multi-scale analysis of temperature field problems. In this manner, a new thermostat is introduced based on the single-atom sub-system, where its capability to control the temperature and produce the canonical ensemble is investigated. Moreover, the performance of proposed thermostat is verified by comparing the distribution of velocities to the Maxwell-Boltzmann distribution. The single-atom sub-system thermostat is then incorporated into the concurrent multi-scale model to relate the temperature field between the continuum and atomistic domains with complex lattice thermal fields. In order to illustrate the capability of proposed coupling continuum–atomistic model, the multi-scale analysis is performed through several numerical examples at various temperature fields and the results are compared with those obtained from the full atomistic model and finite element simulation. Finally, the continuum–atomistic multi-scale technique is applied in numerical simulation of the lattice heat conduction in two-dimensional phononic nano-structures. • A single-atom sub-system thermostat is developed that presents the canonical ensemble. • The performance of proposed thermostat is verified by comparing the velocities distribution to the Maxwell-Boltzmann distribution. • A concurrent multi-scale technique is presented based on the proposed single-atom thermostat. • The concurrent multi-scale technique is applied to model the lattice heat conduction in phononic nano-structures. • The behavior of thermal decay time is investigated for various model parameters in a phononic crystal.