流体流动中运动刚体的4D拓扑优化
4D Topology optimization of moving rigid bodies in fluid flows
AI总结：
本研究将4D拓扑优化框架应用于流体中运动刚体，同步优化其形状与运动，通过数值算例验证了所提方法的有效性。
AI中文摘要：
本研究将4D拓扑优化（一种同时优化系统形态与运动的框架）应用于诱导流体流动的刚体。刚体形状由独立于分析网格的设计网格表示，每个时间步先进行刚体运动，再映射到分析网格；形状采用伪密度法表示，运动直接由离散时间步的位置参数化，并通过时间滤波技术平滑。流体动力学通过格子动力学格式（格子玻尔兹曼方法的扩展版本）评估。通过伴随变量法推导形状与运动的设计灵敏度，优化过程中同步更新形状与运动。最后给出二维和三维数值算例，并从物理角度讨论；通过与仅优化形状或仅优化运动的案例对比，以及多项参数研究，验证了所提方法的有效性。
英文摘要：
This study applies $\textit{4D topology optimization}$, a framework for simultaneously optimizing the morphology and motion of a system, to a rigid body that induces fluid flow. The rigid body shape is represented on a design grid that is independent of the analysis grid, and at each time step, it undergoes rigid-body motion before being mapped onto the analysis grid. The shape is represented using a pseudo-density method, while the motion is directly parametrized by the positions at discrete time steps and smoothed using a temporal filtering technique. The fluid dynamics are evaluated through the lattice kinetic scheme, an extended version of the lattice Boltzmann method. Design sensitivities with respect to both shape and motion are derived via the adjoint variable method, and the shape and motion are intentionally updated simultaneously during the optimization process. Finally, two- and three-dimensional numerical examples are presented and discussed from a physical perspective. Furthermore, the effectiveness of the proposed method is demonstrated by comparison with cases in which only the shape or motion is optimized, as well as through several parameter studies.
