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Topological sensitivity and shape optimization for the Stokes equations. (English) Zbl 1093.49029

Summary: The topological sensitivity analysis provides an asymptotic expansion of a shape function with respect to the insertion of a small hole or obstacle inside a domain. This expansion can then be used for shape optimization. In this paper, such an expansion is obtained for the Stokes equations with general shape functions and arbitrarily shaped holes. A numerical example illustrates the use of the topological sensitivity in a shape optimization problem.

MSC:

49Q10 Optimization of shapes other than minimal surfaces
49Q12 Sensitivity analysis for optimization problems on manifolds
74P05 Compliance or weight optimization in solid mechanics
74P10 Optimization of other properties in solid mechanics
74P15 Topological methods for optimization problems in solid mechanics
76D07 Stokes and related (Oseen, etc.) flows
76D55 Flow control and optimization for incompressible viscous fluids
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