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

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

Hongchul Kim

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.

Keywords


shape control, sensitivity analysis, optimal design, Navier–Stokes equations, drag minimization.

Subject classification

49K40, 49K20, 76D05

Sponsor(s)

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

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