TY - EJOU
AU - Okumura, H.
AU - Kawahara, M.
TI - Shape Optimization of Body Located in Incompressible Navier--Stokes Flow Based on Optimal Control Theory
T2 - Computer Modeling in Engineering \& Sciences
PY - 2000
VL - 1
IS - 2
SN - 1526-1506
AB - 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.
KW - shape optimization
KW - incompressible Navier--Stokes equations
KW - optimal control theory
KW - cyrculaer cylinder
KW - BTD+FS method
KW - LMQN method
KW - finite element method
DO - 10.3970/cmes.2000.001.231