A new stabilized finite element method for shape optimization in the steady Navier--Stokes flow

Authors:
Zhiming Gao;Yichen Ma
Affiliations:
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009-26, Beijing, 100088, PR China;School of Science, Xi'an Jiaotong University, Shaanxi, 710049, PR China
Venue:
Applied Numerical Mathematics
Year:
2010

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Abstract

This paper investigates shape optimization of a solid body located in Navier-Stokes flow in two dimensions. The minimization problem of total dissipated energy is established in the fluid domain. The discretization of Navier-Stokes equations is accomplished using a new stabilized finite element method which does not need a stabilization parameter or calculation of high order derivatives. We derive the structures of 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 formulated and implemented.