A minimization theory in Hilbert space and its application to two-dimensional cavity flow with a numerical study

A minimization theory, which is based on the Hilbert space theory, is proposed and applied to two-dimensional cavity flow past a strut with the assumption of potential flow. That is, the minimization of the cavity drag of the strut on the cavity flow is studied with the help of the optimization theory proposed. To accelerate the optimization process, the Euler beam theory is introduced to generate a small variation in the strut. The introduction of the Euler beam theory makes the mathematical formulation for the present theory ill-conditioned. To overcome this condition, the Tikhonov regularization and the Morozov's discrepancy principle are used to regularize the present optimal theory. From the numerical study, it is shown that the proposed minimization theory is able to find an optimized shape for the given strut and corresponding optimized cavity drag. Received: June 22, 2000 / Accepted: January 30, 2001