Topology optimization of thermal cloak using the adjoint lattice Boltzmann method and the level-set method

This paper presents a topology optimization (TO) method for thermal cloak design based on the adjoint lattice Boltzmann method and the level-set method. The gradient-type TO method presented is of high computational efficiency and of strong parallelism scalability since it completely circumvents large-scale matrix operations. After validated, the TO method is applied to design the thermal cloak composed of common isotropic bulk materials instead of anisotropic meta-materials. A clearly defined material distribution is obtained without non-physical grayscales. Excellent camouflage performance is achieved in the final design with the objective, namely the dimensionless squared norm of the temperature deviation, reduced from 1 to 7.57 × 10⁻⁵. Effects of the dam structures and bypass structures in the designed cloak on the heat transfer are discussed in detail. All results in this work are verified by the finite volume method with the relative error lower than 2 %. A comprehensive parametric study is conducted to reveal the effects of the initial structure, mesh number, thermal conductivity, the subdomain size, as well as the location, shape and topology of the cloaking object. The results have demonstrated the effectiveness, robustness and flexibility of the presented TO method on the practical design of thermal cloak.