We study topology optimization governed by the incompressible Navier-Stokes flows using a phase field model. Novel stabilized semi-implicit schemes for the gradient flows of Allen-Cahn and Cahn-Hilliard types are proposed for solving the resulting optimal control problem. Unconditional energy stability is shown for the gradient flow schemes in continuous and discrete spaces. Numerical experiments of computational fluid dynamics in 2d and 3d show the effectiveness and robustness of the optimization algorithms proposed.

翻译：本文采用相场模型研究由不可压缩Navier-Stokes流控制的拓扑优化问题。针对求解所得最优控制问题，提出了基于Allen-Cahn型与Cahn-Hilliard型梯度流的稳定半隐式新格式。在连续空间与离散空间中均证明了梯度流格式的无条件能量稳定性。二维与三维计算流体动力学数值实验验证了所提优化算法的有效性与鲁棒性。