Body-Fitted Mesh Method for Solving Topology Optimization Problems in Fluid Dynamics

This study aims to develop a high-precision and efficient body-fitted mesh framework for fluid topology optimization, focusing on minimizing flow resistance in incompressible steady Newtonian fluid systems. Different from traditional fixed-mesh methods that suffer from blurred fluid–solid interfaces and numerical dispersion, the proposed work integrates adjoint-based sensitivity analysis, level-set interface evolution, and adaptive body-fitted mesh updating to realize an accurate boundary description and a balanced precision–efficiency performance. The key technologies of body-fitted meshes (initialization, adaptive updating, quality control, and numerical discretization) are elaborated on to form a complete optimization framework. Numerical verification using two classic benchmark problems shows that, compared to traditional non-body-fitted meshes, the proposed method accurately captures the fluid–solid interface, reduces the number of mesh elements by 40–60%, improves computational efficiency by over 30%, and balances numerical precision with cost. These results demonstrate that body-fitted meshing is a promising strategy for high-fidelity and efficient fluid topology optimization.