An efficient and accurate numerical method for the heat conduction problems of thermal metamaterials based on edge-based smoothed finite element method

Thermal metamaterials are a class of artificial composite structures with special thermal conduction properties. Due to the existence of complex multi-phase materials arrangement and interfaces in the thermal metamaterials, an efficient and accurate numerical method is on-demand to predict their temperature distribution and performances. In this paper, we studied the edge-based smoothed finite element method (ES-FEM) for simulating the heat conduction of thermal metamaterials in both steady-state and transient circumstances. Benefit from the adopted smoothing technique, the numerical errors caused by the complex interface are further eliminated. The most significant advantage of the proposed method is that one can directly use the automatically generated coarse triangle mesh to reduce the computational costs while ensuring accuracy. Two numerical examples are presented, in which two typical thermal metamaterials, the thermal cloak and thermal concentration device, are considered respectively in both steady-state and transient cases. The results illustrate that the ES-FEM based approach has good efficiency and accuracy in the heat conduction simulation of the thermal metamaterials.