Nihon Kikai Gakkai ronbunshu (Nov 2018)
Solution to shape identification problems of unsteady viscous flow fields
Abstract
This paper presents a numerical solution to shape identification problems on internal flow and external flow in unsteady viscous flow fields. In the internal flow problem, shape design problem that controlled the flow velocity distribution in the sub-domains of the unsteady viscous flow field was introduced. The square integration error between the actual flow velocity distribution and the target flow velocity distribution in the specified sub-domains was employed as the objective functional for the shape design. In the external flow problem, drag control problem for an isolated body located in uniform flow was formulated in the domain of unsteady viscous flow fields. The shape gradient of these shape identification problems were derived theoretically using the adjoint method, the Lagrange multiplier method and the formulae of the material derivative. Reshaping was accomplished using the traction method that was proposed as a solution to domain optimization problems. Numerical analysis programs for the shape identification problems were developed based on FreeFem++, and the validity of the proposed method was confirmed by the results of 2D numerical analyses.
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