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.

在本文中，在温度场问题的连续-原子多尺度分析中开发了一种新的耦合技术。以这种方式，基于单原子子系统引入了一种新的恒温器，研究了其控制温度和产生规范系综的能力。此外，通过将速度分布与 Maxwell-Boltzmann 分布进行比较，验证了所提出的恒温器的性能。然后将单原子子系统恒温器合并到并发多尺度模型中，以将连续域和原子域之间的温度场与复杂的晶格热场联系起来。为了说明所提出的耦合连续体-原子模型的能力，多尺度分析是通过在不同温度场下的几个数值例子进行的，并将结果与​​从全原子模型和有限元模拟获得的结果进行比较。最后，连续-原子多尺度技术应用于二维声子纳米结构中晶格热传导的数值模拟。