Drag minimization for Navier–Stokes Flow |
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Authors: | Zhiming Gao Yichen Ma Hongwei Zhuang |
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Affiliation: | 1. LCP, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009‐26, Beijing 100088, People's Republic of China;2. School of Science, Xi'an Jiaotong University, Shaanxi 710049, People's Republic of China;3. Engineering College of Armed Police Force, Shaanxi 710086, People's Republic of China |
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Abstract: | This paper investigates the drag minimization in a two‐dimensional flow which is governed by a nonhomogeneous Navier–Stokes equations. Two approaches are utilized to derive shape gradient of the cost functional. The first one is to use the shape derivative of the fluid state and its associated adjoint state; the second one is to utilize the differentiability of a minimax formulation involving a Lagrange functional with a function space parametrization technique. Finally, a gradient type algorithm is effectively formulated and implemented for the mentioned drag minimization problem. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 |
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Keywords: | gradient algorithm minimax principle Navier– Stokes equations shape derivative shape optimization |
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