Optimal shape design is widely used today to improve a variety of designs. It is a challenging task and several methods have been developed. These methods are generally classified by the order of derivatives used. They are zero, first and second order methods, which, as their names imply, use only the function values, first and second order derivatives, respectively. There are two common approaches to first order methods. These are the finite difference method and the adjoint method. The finite difference method requires an additional CFD calculation for each parameter, which quickly becomes computationally very expensive as the number of parameters rise. The adjoint method provides a computationally efficient alternative in such cases. But the computational cost of the adjoint method also becomes expensive if additional constraints are introduced or when multi-objective optimizations are considered.
This paper presents a novel optimization strategy which can be classified as a quasi-gradient based optimization method. As with the finite differences method an additional CFD calculation is performed for each parameter. But in order to save computational time the simulations are not performed to full convergence so that the derivatives are not calculated accurately. The only information that can be obtained in this way is whether the chosen contour manipulation leads to an improvement. A line search method is introduced that can find an optimum using this incomplete gradient information. The optimization method is demonstrated by the quasi-3d optimization of a U-bend.
Pinning-Like Adaptive Consensus for Networked Mobile Agents with Heterogeneous Nonlinear Dynamics
