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.

热超材料是一类具有特殊导热性能的人造复合结构。由于热超材料中存在复杂的多相材料排列和界面，因此需要一种有效且准确的数值方法来预测其温度分布和性能。在本文中，我们研究了基于边缘的平滑有限元方法 (ES-FEM)，用于模拟稳态和瞬态情况下的热超材料的热传导。得益于采用的平滑技术，复杂界面引起的数值误差进一步消除。该方法最显着的优点是可以直接使用自动生成的粗三角网格，在保证精度的同时降低计算成本。给出了两个数值例子，其中在稳态和瞬态情况下分别考虑了两种典型的热超材料，即热斗篷和热浓缩装置。结果表明，基于 ES-FEM 的方法在热超材料的热传导模拟中具有良好的效率和准确性。