Time domain finite element method and numerical simulation of arbitrarily shaped thermal concentrators in metamaterial

To achieve efficient collection and utilization of thermal energy, this paper derives the material parameters for thermally concentrating devices of arbitrary shaped based on transformation thermodynamic principles. A time-domain finite element formulation is then established for the governing equations within the metamaterial region, accompanied by a thorough stability analysis and error estimation of the numerical algorithm. Finally, numerical simulation experiments are conducted to validate both the correctness of the derived material parameters and the effectiveness of the proposed numerical scheme.