4D Topology optimization of moving rigid bodies in fluid flows

Abstract

This study applies $\textit{4D topology optimization}$, a framework for simultaneously optimizing the morphology and motion of a system, to a rigid body that induces fluid flow. The rigid body shape is represented on a design grid that is independent of the analysis grid, and at each time step, it undergoes rigid-body motion before being mapped onto the analysis grid. The shape is represented using a pseudo-density method, while the motion is directly parametrized by the positions at discrete time steps and smoothed using a temporal filtering technique. The fluid dynamics are evaluated through the lattice kinetic scheme, an extended version of the lattice Boltzmann method. Design sensitivities with respect to both shape and motion are derived via the adjoint variable method, and the shape and motion are intentionally updated simultaneously during the optimization process. Finally, two- and three-dimensional numerical examples are presented and discussed from a physical perspective. Furthermore, the effectiveness of the proposed method is demonstrated by comparison with cases in which only the shape or motion is optimized, as well as through several parameter studies.