A topology optimization method for steady-state flows of incompressible fluids which is capable of imposing accurate boundary conditions along the solid walls of the sought fluid paths is presented. In each topology optimization cycle, body-conforming Cartesian meshes are generated around shapes of any complexity by tracing the fluid-solid interfaces and a cut-cell flow solver is implemented together with its adjoint. Sensitivity derivatives are computed along the fluid-solid interfaces via the continuous adjoint method. Changes in topology are caused by expressing the computed sensitivity derivatives w.r.t. an auxiliary background material distribution, that helps updating the fluid-solid interfaces. The proposed method performance is assessed on three 2D benchmark examples and a 3D case. Two out of the three 2D examples are also solved using a porosity-based topology optimization approach in which impermeable regions are penalized by a Brinkman term and useful conclusions are drawn. For a fair comparison, designs optimized using the porosity-based method are re-evaluated after extracting fluid-solid interfaces from the computed porosity fields.

提出了一种用于不可压缩流体稳态流动的拓扑优化方法，该方法能够沿所寻求的流体路径的实体壁施加准确的边界条件。在每个拓扑优化循环中，通过跟踪流体-固体界面，围绕任何复杂形状生成符合体的笛卡尔网格，并与它的伴随物一起实施切割单元流动求解器。通过连续伴随法沿流固界面计算灵敏度导数。拓扑结构的变化是由将计算的灵敏度导数表达为辅助背景材料分布引起的，这有助于更新流固界面。所提出的方法性能在三个 2 D基准示例和一个 3 D案件。三个二维示例中的两个也使用基于孔隙度的拓扑优化方法求解，其中不可渗透区域受到 Brinkman 项的惩罚，并得出有用的结论。为了公平比较，在从计算的孔隙度场中提取流固界面后，重新评估使用基于孔隙度的方法优化的设计。