Control of Euler and Navier-Stokes equations: Applications to optimal shape design in aeronautics

2007 ◽  
Author(s):  
Carlos Castro ◽  
Carlos Lozano ◽  
Francisco Palacios ◽  
Enrique Zuazua
Keyword(s):  
Stokes Equations ◽  
Optimal Shape ◽  
Navier Stokes ◽  
Shape Design ◽  
Optimal Shape Design ◽  
Navier Stokes Equations

Optimal Shape Design of a Body Located in Stokes Flow

2011 ◽  
Vol 320 ◽  
pp. 303-308
Author(s):  
Xian Bao Duan ◽  
Fu Cai Qian ◽  
Ya Qin Guo
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Optimal Shape ◽  
The Body ◽  
Shape Design ◽  
Optimal Shape Design ◽  
Shape Sensitivity ◽  
Initial State ◽  
Cost Functional ◽  
The Cost

Formulations and numerical results for optimal shape design of a body located in the incompressible Stokes fluid flow are presented. The study is based on an optimal control theory. The optimal state is defined by the reduction of drag forces subjected to the body. The cost functional should be minimized satisfying the Stokes equations. The Shape sensitivity analysis of the cost functional was derived based on the adjoint method. For the numerical study, the optimal shape of the body which has a circular shape as an initial state can be finally obtained as the streamlined shape.

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