First- and second-order sensitivity equation methods for value and shape parameters
This paper presents formulations of the sensitivity equation method (SEM) and applications to transient flow problems. Solutions are shown for both value and shape parameters using a three-dimensional solution algorithm. Sensitivities are used for fast evaluation of the flow at nearby values of the parameters: the solution is approximated by a Taylor series in parameter space involving the flow sensitivities. The accuracy of nearby flows is much improved when second-order sensitivities are used. We show how the sensitivity of the Strouhal number can be obtained from the flow sensitivities. Results are in agreement with the experimental correlation. The methodology is also applied to the flow past a cylinder in ground proximity. The proposed method is verified on a steady-state problem by comparing the computed sensitivity with the actual change in the solution when a small perturbation is imposed on the shape parameter. We then investigate the ability of the SEM to anticipate the unsteady flow response to changes in the ground to cylinder gap. The approach properly reproduces the damping or amplification of the vortex shedding with a reduction or increase of the gap size. Copyright (C) 2008 Crown in the right of Canada. Published by John Wiley & Sons, Ltd.
second-order sensitivity sensitivity equations three-dimensional finite elements time-dependent flows shape sensitivity incompressible flows