Shape optimization of a body in the Oseen flow |
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Authors: | Axia Wang Yichen Ma Zhiming Gao |
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Affiliation: | 1. School of Science, Xi'an Jiaotong University, Xi'an, Shaanxi, People's Republic of China, 710049;2. School of Science, Chang'an University, Xi'an, Shaanxi, People's Republic of China, 710064;3. Institute of Applied Physics and Computational Mathematics, Beijing, People's Republic of China, 100088 |
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Abstract: | This article is concerned with a numerical simulation of shape optimization of the Oseen flow around a solid body. The shape gradient for shape optimization problem in a viscous incompressible flow is computed by the velocity method. The flow is governed by the Oseen equations with mixed boundary conditions containing the pressure. The structure of continuous shape gradient of the cost functional is derived by using the differentiability of a minimax formulation involving a Lagrange functional with a function space parametrization technique. A gradient type algorithm is applied to the shape optimization problem. Numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 |
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Keywords: | gradient algorithm minimax formulation shape optimization the Oseen equations |
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