Abstract
This paper presents a numerical solution to multipurpose shape optimization problems of steady state viscous flow fields. In previous study, it has been dealt with drag minimization problems and lift maximization problems for an isolated body located in uniform flow in viscous flow fields. In this study, multipurpose shape optimization problem using normalized objective functional is formulated for the drag minimization and the lift maximization. Shape gradient of the shape optimization problem was derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Reshaping was carried out by the traction method proposed as an approach to solving shape optimization problems. The validity of proposed method was confirmed by results of 2D low-Reynolds number viscous flow problems.
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