Multi-Objective Shape Optimization for Drag Minimization and Lift Maximization in Low Reynolds Number Flows

摘要

This paper presents a numerical solution to multi-objective shape optimization problems of steady-state viscous flow fields. In this study, a multi-objective shape optimization problem using a normalized objective functional is formulated for drag minimization and lift maximization of an isolated body located in viscous uniform flow. In addition, another multi-objective shape optimization problem is formulated for lift maximization while the drag is set to a desired constant value. The shape gradients for these shape optimization problems are derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Reshaping is performed using the traction method, which has been proposed as an approach to solving shape optimization problems. The validity of the proposed method is confirmed by the results of 2D low Reynolds number viscous flow problems.