Shape optimization for Stokes flow

Authors:
Zhiming Gao;Yichen Ma;Hongwei Zhuang
Affiliations:
School of Science, Xi'an Jiaotong University, P.O. Box 1844, Xi'an, Shaanxi, P.R. China, 710049;School of Science, Xi'an Jiaotong University, P.O. Box 1844, Xi'an, Shaanxi, P.R. China, 710049;Engineering College of Armed Police Force, Shaanxi, P.R. China, 710086
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

This paper is concerned with a shape sensitivity analysis of a viscous incompressible fluid driven by Stokes equations. The structures of continuous shape gradients with respect to the shape of the variable domain for some given cost functionals are established by introducing the Piola transformation and then deriving the state derivative and its associated adjoint state. Finally we give the finite element approximation of the problem and a gradient type algorithm is effectively used for our problem.