Korean J. Math. Vol. 25 No. 3 (2017) pp.405-435
DOI: https://doi.org/10.11568/kjm.2017.25.3.405

Sensitivity analysis of a shape control problem for the Navier--Stokes equations

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Published: Sep 30, 2017
Keywords:
shape control, sensitivity analysis, optimal design, Navier–Stokes equations, drag minimization.
Mathematics Subject Classification:
Navier–Stokes equations, 49K40, 49K20, 76D05

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Hongchul Kim
Department of Mathematics Gangneung-Wonju National University

Abstract

We deal with a sensitivity analysis of an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. By using the material derivative method and adjoint variables for a shape sensitivity analysis, we derive the shape gradient of the design functional for the model problem.


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Supporting Agencies

This paper was supported in part by the Research Institute of Natural Science of Gangneung-Wonju National University.

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