This paper proposes a topology optimization method for non-thermal and thermal fluid problems using the Lattice Kinetic Scheme (LKS).LKS, which is derived from the Lattice Boltzmann Method (LBM), requires only macroscopic values, such as fluid velocity and pressure, whereas LBM requires velocity distribution functions, thereby reducing memory requirements. The proposed method computes design sensitivities based on the adjoint variable method, and the adjoint equation is solved in the same manner as LKS; thus, we refer to it as the Adjoint Lattice Kinetic Scheme (ALKS). A key contribution of this method is the proposed approximate treatment of boundary conditions for the adjoint equation, which is challenging to apply directly due to the characteristics of LKS boundary conditions. We demonstrate numerical examples for steady and unsteady problems involving non-thermal and thermal fluids, and the results are physically meaningful and consistent with previous research, exhibiting similar trends in parameter dependencies, such as the Reynolds number. Furthermore, the proposed method reduces memory usage by up to 75% compared to the conventional LBM in an unsteady thermal fluid problem.

翻译：本文提出了一种利用格子动力学格式（LKS）处理非热流体与热流体问题的拓扑优化方法。LKS源于格子玻尔兹曼方法（LBM），但仅需宏观量（如流体速度与压力），而LBM则需要速度分布函数，从而显著降低了内存需求。所提方法基于伴随变量法计算设计灵敏度，其伴随方程采用与LKS相同的求解方式，因此我们将其称为伴随格子动力学格式（ALKS）。该方法的一个关键贡献在于提出了伴随方程边界条件的近似处理方案，由于LKS边界条件的特性，直接施加边界条件具有挑战性。我们通过稳态与非稳态的非热流体及热流体数值算例进行验证，结果表明优化结果具有物理意义且与已有研究相符，在雷诺数等参数依赖性上呈现出相似的趋势。此外，在非稳态热流体问题中，与传统的LBM相比，所提方法的内存使用量最高可减少75%。