报告题目 (Title)：Energy stable gradient flow schemes for shape and topology optimization in Navier-Stokes flows
中文题目：纳维-斯托克斯流中形状和拓扑优化的能量稳定梯度流格式
报告人 (Speaker)：李嘉杰 （吴文俊助理教授，上海交通大学）
报告时间 (Time)：2024年11月28日 (周四) 10:00
报告地点 (Place)：校本部D109
邀请人(Inviter)：纪丽洁
主办部门：理学院数学系
摘要：We study topology optimization governed by the incompressible Navier-Stokes equations using a phase field model. Unconditional energy stability is shown for the gradient flow in continuous space. The novel generalized stabilized semi-implicit schemes for the gradient flow in first-order time discretization of Allen-Cahn and Cahn-Hilliard types are proposed to solve the resulting optimal control problem. With the Lipschitz continuity for state and adjoint variables, the energy stability for time and full discretization has been proved rigorously on condition that the stabilized parameters are larger than given numbers. The proposed gradient flow scheme has the capability to work with large time steps and exhibits a constant coefficient system in full discretization which can be solved efficiently. Numerical examples in 2d and 3d show the effectiveness and robustness of the optimization algorithms proposed.
