APPLYING A PHASE FIELD APPROACH FOR SHAPE OPTIMIZATION OF A STATIONARY NAVIER-STOKES FLOW

作者：Garcke Harald^*; Hecht Claudia^*

来源：ESAIM: Control, Optimisation and Calculus of Variations , 2016, 22(2): 309-337.

DOI：10.1051/cocv/2015006

• Shape and topology optimization
• phase field method
• diffuse interfaces
• stationary Navier-Stokes flow
• fictitious domain

We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes flow. To be precise we add a multiple of the Ginzburg-Landau energy as a regularization to the objective functional and relax the non- permeability of the medium outside the fluid region. The resulting diffuse interface problem can be shown to be well-posed and optimality conditions are derived. We state suitable assumptions on the problem in order to derive a sharp interface limit for the minimizers and the optimality conditions. Additionally, we can derive a necessary optimality system for the sharp interface problem by geometric variations without stating additional regularity assumptions on the minimizing set.

• 出版日期2016-6