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The application of adjoint method for shape optimization in Stokes–Oseen flow
Author(s) -
Yan Wenjing,
Gao Zhiming
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4039
Subject(s) - shape optimization , mathematics , stokes flow , flow (mathematics) , balanced flow , reynolds number , parametrization (atmospheric modeling) , adjoint equation , work (physics) , mathematical optimization , incompressible flow , navier–stokes equations , space (punctuation) , compressibility , mathematical analysis , geometry , partial differential equation , computer science , mechanics , finite element method , physics , quantum mechanics , turbulence , thermodynamics , radiative transfer , operating system
This paper presents a numerical method for shape optimization of a body immersed in an incompressible viscous flow governed by Stokes–Oseen equations. The purpose of this work is to optimize the shape that minimizes a given cost functional. Based on the continuous adjoint method, the shape gradient of the cost functional is derived by involving a Lagrangian functional with the function space parametrization technique. Then, a gradient‐type algorithm is applied to the shape optimization problem. The numerical examples indicate the proposed algorithm is feasible and effective in low Reynolds number flow. Copyright © 2016 John Wiley & Sons, Ltd.