Topology optimization for lift-drag problems incorporated with distributed unstructured mesh adaptation

作者：Li, Hao^*; Kondoh, Tsuguo; Jolivet, Pierre; Nakayama, Nari; Furuta, Kozo; Zhang, Heng; Zhu, Benliang; Izui, Kazuhiro; Nishiwaki, Shinji

来源：STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, 2022, 65(8): 222.

DOI：10.1007/s00158-022-03314-w

• Topology optimization
• Lift-drag
• Distributed unstructured mesh adaptation
• Isotropic mesh
• Anisotropic mesh
• Level-set method (LSM)
• FreeFEM
• ParMmg

This note introduces the distributed unstructured mesh adaptation into the fluid-related topology optimization which is a first step in that direction. We incorporate three different remeshing techniques (isotropic, anisotropic, or body-fitted adaptive mesh refinement) into the reaction-diffusion equation-based fluid topology optimization method. It requires a fully distributed framework (including scalable domain decomposition, matrix assembly, parallel interpolation, linear solver) that very few general purpose libraries offer. In addition, this note is the first attempt to conduct a comparative study by showcasing two different flow modeling strategies with their advantages and disadvantages. More specifically, the "separate" modeling, relying on the surface-capturing technique, i.e., body-fitted mesh, allows the disjoint reunion of a global mesh that contains several (fluid/solid) subdomains. The no-slip boundary conditions can be applied on the moving fluid-solid interface. The "hybrid" modeling, on the other hand, relying on the monolithic formulation, can be incorporated with iso-/anisotropic meshes. For comparison and for accessing the constructed framework, a lift-drag optimization problem and a classical minimal power dissipation problem are formulated. Various two- and three-dimensional numerical examples are presented to validate the computational efficiency of this framework.