Abstract A derivative-free level-set-based topology optimization method (DFLS-TO) was proposed and was used for channel structure design. Unlike in a conventional level-set method, quantum-behaved particle swarm optimization (QPSO) was used in DFLS-TO to optimize the level-set values at the knot points. The values at the non-knot points were interpolated by solving the Laplace equation. QPSO was combined with the Tchebycheff decomposition method to search for optimal level-set values in multi-objective problems. The channel boundary was represented by an iso-contour of the level-set function, and the B-spline method was used to convert the zigzag-like boundary into a smooth boundary. The lattice Boltzmann method (LBM) was integrated with the immersed boundary method to simulate the fluid flow. The Spalart–Allmaras model was incorporated with the LBM during the simulation of turbulent flows. To demonstrate the applicability of DFLS-TO, optimization of a pipe bend and a fluid distributor were performed.

中文翻译：

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使用格子 Boltzmann 方法的流道设计的基于无导数水平集的多目标拓扑优化

摘要 提出了一种基于水平集的无导数拓扑优化方法(DFLS-TO)，并将其用于信道结构设计。与传统的水平集方法不同，在 DFLS-TO 中使用量子行为粒子群优化 (QPSO) 来优化节点处的水平集值。通过求解拉普拉斯方程对非结点处的值进行插值。QPSO 与 Tchebycheff 分解方法相结合，在多目标问题中寻找最优水平集值。通道边界由水平集函数的等值线表示，并使用B样条方法将之字形边界转换为平滑边界。格子 Boltzmann 方法 (LBM) 与浸入边界方法相结合以模拟流体流动。在模拟湍流过程中，Spalart-Allmaras 模型与 LBM 相结合。为了证明 DFLS-TO 的适用性，我们对弯管和流体分配器进行了优化。