Shape optimization for an obstacle located in incompressible Boussinesq flow

• Published in: Computers & fluids 2022-05, Vol.240, p.105431, Article 105431
• Main Authors: Yan, Wenjing, Li, Yingyuan, Hou, Jiangyong
• Format: Article
• Language: English
• Subjects: Adjoint method; Barriers; Boussinesq equations; Continuity (mathematics); Energy dissipation; Fluid flow; Function space; Function space parametrization; Incompressible flow; Incompressible fluids; Inverse problems; Optimal control; Parameterization; Shape gradient; Shape inverse design; Shape optimal control; Shape optimization
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2022.105431

In this paper, the shape optimal control for an obstacle immersed in the incompressible fluid governed by Boussinesq equations is investigated. The purpose of this work is to find the optimal shape that minimizes two types of cost functionals. The continuous adjoint method is applied to formulate and implement the nonlinear and strongly coupled system, which can avoid the differentiation of the state system. Then, the Eulerian derivative of the cost functional is derived by involving a Lagrangian functional based on the function space parametrization technique. Finally, the numerical examples of the shape inverse problem and the minimization of energy dissipation are presented to verify the feasibility and effectiveness of the proposed method. •Shape optimization of the nonlinear and strongly coupled system is considered based on the continuous adjoint method.•Eulerian derivative for the cost functional is obtained by the velocity method and function space parametrization technique.•The designed method can reduce the computation cost while ensuring the high accuracy.•Numerical examples are performed to demonstrate the feasibility and effectiveness of the proposed method.