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This work is concerned with a geometric inverse problem in fluid mechanics. The aim is to reconstruct an unknown obstacle immersed in a Newtonian and incompressible fluid flow from internal data. We assume that the fluid motion is governed by the Stokes-Brinkmann equations in the two dimensional case. We propose a simple and efficient reconstruction method based on the topological sensitivity concept. The geometric inverse problem is reformulated as a topology optimization one minimizing a least-square functional. The existence and stability of the optimization problem solution are discussed. A topological sensitivity analysis is derived with the help of a straightforward approach based on a penalization technique without using the classical truncation method. The theoretical results are exploited for building a non-iterative reconstruction algorithm. The unknown obstacle is reconstructed using a level-set curve of the topological gradient. The accuracy and the robustness of the proposed method are justified by some numerical examples.
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참고문헌 (33)
참고문헌 신청
G. Allaire / 2004 / Topology optimization with the homogenization and the level-set methods, in Nonlinear homogenization and its applications to composites, polycrystals and smart materials / NATO Sci. Ser. II Math. Phys. Chem. 170:1~13
G. Allaire / 2004 / Structural optimization using sensitivity anal-ysis and a level-set method / J. Comput. Phys. 194(1):363~393
C. J. S. Alves / 2004 / On the determination of point-forces on a Stokes system / Math. Comput. Simulation 66(4-5):385~397
L. Ambrosio / 2000 / Oxford Mathematical Monographs / The Clarendon Press, Oxford University Press
S. Amstutz / 2005 / The topological asymptotic for the Navier-Stokes equations / ESAIM Control Optim. Calc. Var. 11(3):401~425
G. Allaire / 2004 / Structural optimization using sensitivity anal-ysis and a level-set method / J. Comput. Phys. 194(1):363~393
C. J. S. Alves / 2004 / On the determination of point-forces on a Stokes system / Math. Comput. Simulation 66(4-5):385~397
L. Ambrosio / 2000 / Oxford Mathematical Monographs / The Clarendon Press, Oxford University Press
S. Amstutz / 2005 / The topological asymptotic for the Navier-Stokes equations / ESAIM Control Optim. Calc. Var. 11(3):401~425
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