Optimal Shape Design for the Time-dependent Navier--Stokes Flow

Details Optimal Shape Design for the Time-dependent Navier--Stokes Flow Optimal Shape Design for the Time-dependent Navier--Stokes Flow

2006-12-06

arxiv.org/abs/math/0612154v1

Mathematics

Optimization and Control

22 pages, 5 figures

Scientific paper

This paper is concerned with the problem of shape optimization of two-dimensional flows governed by the time-dependent Navier-Stokes equations. We derive the structures of shape gradients with respect to the shape of the variable domain for time-dependent cost functionals by using the state derivative with respect to the shape of the fluid domain and its associated adjoint state. Finally we apply a gradient type algorithm to our problem and numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible in low Reynolds number flow.

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