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Optimal shape design for fluid flow using topological perturbation technique. (English) Zbl 1172.35049
Summary: This paper is concerned with an optimal shape design problem in fluid mechanics. The fluid flow is governed by the Stokes equations. The theoretical analysis and the numerical simulation are discussed in two and three-dimensional cases. The proposed approach is based on a sensitivity analysis of a design function with respect to the insertion of a small obstacle in the fluid flow domain. An asymptotic expansion is derived for a large class of cost functions using small topological perturbation technique. A fast and accurate numerical algorithm is proposed. The efficiency of the method is illustrated by some numerical examples.

MSC:
35Q30 Navier-Stokes equations
35C20 Asymptotic expansions of solutions to PDEs
76M10 Finite element methods applied to problems in fluid mechanics
49J20 Existence theories for optimal control problems involving partial differential equations
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