Solution to shape identification problems of unsteady viscous flow fields

This paper presents numerical solution to a shape optimization of viscous flow field for stationary fluid-structureinteractive (FSI) fields. In the FSI analysis, a weak coupled analysis is used to alternately analyze the governing equations of the flow field domain and the structural field considering geometrically nonlinear. A minimization problem for total dissipation energy is formulated for the shape optimization of viscous flow field in the FSI fields. Shape gradient of the shape optimization problem is derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Reshaping is carried out by the H 1 gradient method proposed as an approach to solving shape optimization problems. For shape optimization of the viscous flow field in the FSI fields, a new shape update method is proposed to overcome separation and interference of the finite element meshes on the common boundary between the flow field and the structural field. Numerical analysis program for the shape optimization problem is developed by using FreeFEM, and the validity of proposed method is confirmed by results of 2D numerical analyses.

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Shape optimization of viscous flow field considering fluid-structure-interactive

Katamine

Kawai

Yamashita

2021

Transactions of the JSME (In Japanese)

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Shape optimization of viscous flow domain considering unsteady fluid structure interaction

KATAMINE,

SHIMAKAWA

2023

Transactions of the JSME (In Japanese)

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This paper presents numerical solution to shape design problems of viscous flow field for unsteady fluid-structureinteractive (FSI) fields. In the FSI analysis, a strong coupled analysis is used to analyze the governing equation of the flow domain and the structural domain considering nonlinearity of strain. A minimization problem for total dissipation energy is formulated for the shape optimization of viscous flow domain in the FSI fields. Also, a shape design problem is formulated to control the flow velocity distribution in the sub-domains of the flow domain. This latter problem can be treated as an inverse problem for minimizing the square error integration between the actual flow velocity distribution and the target flow velocity distribution in the sub-domains. Shape gradient of these shape design problems are derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative.Reshaping is carried out by the H 1 gradient method proposed as an approach to solving shape optimization problems.Numerical analysis programs for these shape optimization problems are developed by using FreeFEM, and the validity of proposed method is confirmed by results of 2D numerical analyses.

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Solution to shape identification problems of unsteady viscous flow fields

Cited by 2 publications

References 23 publications

Shape optimization of viscous flow field considering fluid-structure-interactive

Shape optimization of viscous flow field considering fluid-structure-interactive

Shape optimization of viscous flow domain considering unsteady fluid structure interaction

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