Shape optimization for an obstacle located in incompressible Boussinesq flow. (English) Zbl 1521.76126
Summary: 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.
MSC:
| 76D55 | Flow control and optimization for incompressible viscous fluids |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76M30 | Variational methods applied to problems in fluid mechanics |
Keywords:
shape optimal control; shape inverse design; Boussinesq equations; shape gradient; adjoint method; function space parametrizationReferences:
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