发表机构
Jiujiang University; Dalian University of Technology; Karlsruhe Institute of Technology (KIT); Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP), Chinese Academy of Sciences; University of Chinese Academy of Sciences（九江学院; 大连理工大学; 卡尔斯鲁厄理工学院; 中国科学院长春光学精密机械与物理研究所; 中国科学院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种扩散界面公式的密度拓扑优化框架，处理稳态纳维-斯托克斯流中设计依赖的壁面驱动，通过解析源系数和伴随灵敏度实现流量最大化，并扩展至电渗输运。
AI 中文摘要
设计依赖的壁面速度在基于密度的流体拓扑优化中难以处理。这一困难源于流体-固体界面被隐式表示，并随设计演化。本文提出一种用于稳态不可压缩纳维-斯托克斯流拓扑优化的扩散界面公式，其中包含设计依赖的壁面驱动。由紧支撑径向基函数（CS-RBFs）参数化的连续拓扑描述场提供局部界面方向，其正则化投影定义用于Brinkman流分析的伪密度。壁面速度通过等效体积动量源施加在固定网格上，该动量源由基于伪密度和描述场梯度构建的扩散界面测度局部化。假设局部平面界面和均匀分布的Wendland径向基函数，通过平衡界面中心处的等效动量输入与Brinkman阻力，解析确定源系数。这些假设还给出了以投影陡度和支撑半径表示的特征过渡宽度估计。进行连续伴随分析以推导设计灵敏度。使用类比方程公式化的二维和三维算例证明了所提出的拓扑优化方法在流量最大化方面的有效性。贴体网格重仿真验证了优化设计的流场和输运性能。该公式进一步扩展至薄电双层（EDL）假设下的电渗输运，使用Helmholtz-Smoluchowski关系。
英文摘要
Design-dependent wall velocities are difficult to treat in density-based fluid topology optimization. This difficulty arises because the fluid-solid interface is represented implicitly and evolves with the design. This paper proposes a diffuse-interface formulation for topology optimization of steady incompressible Navier-Stokes flows with design-dependent wall actuation. A continuous topological description field parameterized by compactly supported radial basis functions (CS-RBFs) provides the local interface orientation, and its regularized projection defines the pseudo-density for Brinkman flow analysis. The wall velocity is imposed on a fixed mesh through an equivalent volumetric momentum source, which is localized by a diffuse-interface measure constructed from the pseudo-density and the gradient of the description field. Assuming a locally planar interface and uniformly distributed Wendland radial basis functions, the source coefficient is determined analytically by balancing the equivalent momentum input with the Brinkman resistance at the interface center. These assumptions also yield a characteristic transition-width estimate in terms of the projection steepness and support radius. Continuous adjoint analysis is performed to derive the design sensitivities. Two- and three-dimensional examples formulated using the analogy equation demonstrate the effectiveness of the proposed topology optimization method for flow-rate maximization. Body-fitted re-simulations verify the flow fields and transport performance of the optimized designs. The formulation is further extended to electroosmotic transport under the thin electric double layer (EDL) assumption using the Helmholtz-Smoluchowski relation.
