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Unsteady flow optimization by a stabilized finite element method
Author(s) -
Gao Zhiming,
Ma Yichen
Publication year - 2010
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1284
Subject(s) - discretization , finite element method , mathematics , navier–stokes equations , flow (mathematics) , mathematical optimization , shape optimization , eulerian path , mathematical analysis , domain (mathematical analysis) , mechanics , geometry , physics , compressibility , lagrangian , thermodynamics
This paper presents the problem of shape optimization of two‐dimensional viscous flow governed by the time‐dependent Navier–Stokes equations. The minimization problem of the viscous dissipated energy was established in the fluid domain. The discretization of Navier–Stokes equations is accomplished using a new stabilized finite element method in space and finite difference in time. This new method does not need a stabilization parameter or calculation of high‐order derivatives. We derive the structures of the discrete Eulerian derivative of the cost functional by a discrete adjoint method with a function space parametrization technique. A gradient‐type optimization algorithm with a mesh adaptation technique and a mesh moving strategy is effectively implemented. Copyright © 2009 John Wiley & Sons, Ltd.