Topology optimization of actively moving rigid bodies in unsteady flows

TL;DR

This paper introduces a new topology optimization approach for actively moving rigid bodies in unsteady flows, using separate design and analysis grids and a lattice kinetic scheme for efficient sensitivity analysis.

Contribution

It presents a decoupled grid method for representing complex object motions in unsteady flows, enhancing computational efficiency and flexibility in topology optimization.

Findings

Validated the accuracy of sensitivity calculations against finite differences.

Demonstrated effectiveness through 2D and 3D numerical examples.

Abstract

This study proposes a novel topology optimization method for unsteady fluid flows induced by actively moving rigid bodies. The key idea of the proposed method is to decouple the design and analysis domains by using separate grids. The design grid undergoes rigid body motion and is then overlapped onto the analysis grid. After the overlap, key quantities such as the Brinkman coefficient are transferred between the grids. This approach provides a direct and efficient means of representing object motion and facilitates the handling of more general and complex movements in unsteady flow conditions. Since the computational cost of solving unsteady fluid problems is substantial, we employ a solver based on the lattice kinetic scheme, which is the extended version of the lattice Boltzmann method, to evaluate the design sensitivity. The fundamental equations are derived, and the accuracy of the design sensitivity calculations is validated through comparison with finite difference approximations. The effectiveness of the method is demonstrated through numerical examples in two-dimensional and three-dimensional settings.