Large-Scale Topology Optimization for Unsteady Flow Using the Building-Cube Method

In recent years, topology optimization methods have been applied not only to structural problems but also to fluid flow problems. Most of the previous studies assume steady-state flow. In contrast, this paper focuses on topology optimization for unsteady flow, which is more general from an engineering point of view. However, unsteady flow topology optimization involves solving the governing and adjoint equations of a time-evolving system, which requires a huge computational cost for topology optimization with a fine mesh. Therefore, we propose a large-scale unsteady flow topology optimization based on the building-cube method (BCM), which is suitable for massively parallel computing. BCM is one of the hierarchical Cartesian mesh methods and is confirmed to have very good scalability. The governing equations are discretized by a cell-centered finite volume method based on the BCM. The objective sensitivity is obtained by the continuous adjoint method. Several numerical examples are demonstrated to discuss its applicability to large-scale computations. © 2023 by the Japan Society for Computational Engineering and Science.