Shape optimization of unsteady state viscous flow fields for drag minimization and lift maximization

Abstract

This paper describes a numerical solution to the shape optimization problems of viscous flow fields. The drag minimization problem and lift maximization problem for an isolated body in uniform flow were formulated in the domain of unsteady-state viscous flow fields. The shape gradient of the shape optimization problems were derived theoretically using the adjoint variable method, the Lagrange multiplier method and the formulae of the material derivative. Reshaping was accomplished using a traction method that was proposed as a solution to domain optimization problems. Numerical analyses program for the shape optimization is developed based on FreeFem++, and the validity of proposed method is confirmed by results of 2D numerical analyses.