Solution to shape optimization problems of viscous flow fields

Abstract

This paper presents a numerical solution to the shape optimization problems of steady-state viscous flow fields. The minimization problem of total dissipation energy was formulated in the domain of viscous flow fields. The shape gradient of the shape optimization problem was derived theoretically using the adjoint variable method, the Lagrange multiplier method and the formulae of the material derivative. Reshaping was carried out by the traction method proposed by one of the authors as an approach to solving domain optimization problems. The validity of the proposed method was confirmed by results of 2D and 3D numerical analyses.

Keywords:

• Shape optimization
• Optimum design
• Computational fluid dynamics
• Finite-element method
• Shape gradient
• Adjoint variable method

Acknowledgements

This study was financially supported by the Research Foundation for Electrotechnology of Chubu in Japan.

Additional information

Notes on contributors

Eiji Katamine