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Shape Optimization of Body Located in Incompressible Navier--Stokes Flow Based on Optimal Control Theory

H. Okumura1, M. Kawahara1
Department of Civil Engineering, Chuo University; Kasuga 1-13-27, Bunkyo-ku, Tokyo 112-8551, Japan.

Computer Modeling in Engineering & Sciences 2000, 1(2), 71-78.


This paper presents a new approach to a shape optimization problem of a body located in the unsteady incompressible viscous flow field based on an optimal control theory. The optimal state is defined by the reduction of drag and lift forces subjected to the body. The state equation used is the transient incompressible Navier--Stokes equations. The shape optimization problem can be formulated to find out geometrical coordinates of the body to minimize the performance function that is defined to evaluate forces subjected to the body. The fractional step method with the implicit temporal integration and the balancing tensor diffusivity (BTD) formulation are employed for the discretization with the equal--order finite element approximation, while the Crank--Nicolson scheme is used for the temporal discretization. LMQN (Limited-memory quasi--Newton) method, which is an iterative procedure saving the computational memory, is applied for minimizing the performance function. For the numerical study, the optimal shape of the body which has circular shape as the initial state can be finally obtained as the streamlined shape.


shape optimization, incompressible Navier--Stokes equations, optimal control theory, cyrculaer cylinder, BTD+FS method, LMQN method, finite element method

Cite This Article

Okumura, H., Kawahara, M. (2000). Shape Optimization of Body Located in Incompressible Navier--Stokes Flow Based on Optimal Control Theory. CMES-Computer Modeling in Engineering & Sciences, 1(2), 71–78.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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