On the identification of a rigid body immersed in a fluid: A numerical approach

Álvarez, Catalina; Conca, Carlos; Lecaros, Rodrigo; Ortega, Juan‐Pablo

doi:10.1016/j.enganabound.2007.02.007

Cited by 12 publications

(59 citation statements)

References 6 publications

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“…Applying theorem 1, we deduce that for any u * ∈ H 3/2 (∂ ) such that (12) holds, there exist T (1) * > 0 (respectively T (2) * > 0) and a unique solution (a (1) , Q (1) , (1) , ω (1) , u (1) , p (1) ) (respectively (a (2) , Q (2) , (2) , ω (2) , u (2) , p (2) )) of (2)- (11) in [0, T (1) * ) (respectively in [0, T (2) * )).…”

Section: Resultsmentioning

confidence: 94%

“…Now, let us take two smooth non-empty domains S (1) 0 and S (2) 0 . Let us also consider a (1) 0 , Q (1) 0 , a (2) 0 , Q (2) 0 (1) 0 , Q (1) 0 ⊂ and S (2) a (2) 0 , Q (2) 0 ⊂ .…”

Section: Resultsmentioning

confidence: 99%

“…In the above theorem, the hypothesis of convexity for the obstacle is technical and could probably be removed. The hypothesis t 0 < min(T (1) * , T (2) * ) means that we observe our data before any contact between the rigid body and the exterior boundary ∂ .…”

Section: Theoremmentioning

confidence: 93%

“…With the above notation, assume that u * ∈ H 3/2 (∂ ) satisfies (12) and u * is not the trace of a rigid velocity on . Assume also that S (1) 0 and S (2) 0 are convex. If there exists 0 < t 0 < min(T (1) * , T (2) * ) such that σ(u (1) (1) (2) (2) (1) 0 = S (2) 0 and a (1) 0 = a (2) 0 , Q (1) 0 = Q (2) 0 R. In particular, T (1) * = T (2) * and S (1)…”

Section: Theoremmentioning

confidence: 99%

“…In this paper, we show the identifiability of S 0 , proving that to each measurement of the Cauchy forces on , there is a corresponding shape S 0 , which is unique up to a rotation matrix. More precisely, let us take two non-empty open sets S (1) 0 and S (2) 0 . We prove that under certain assumptions on the rigid bodies and the function u * , we can identify the structure (see theorem 2).…”

Section: Introductionmentioning

confidence: 99%

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On the identifiability of a rigid body moving in a stationary viscous fluid

Conca¹,

Schwindt²,

Takahashi³

2011

Inverse Problems

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This paper is devoted to a geometrical inverse problem associated with a fluidstructure system. More precisely, we consider the interaction between a moving rigid body and a viscous and incompressible fluid. Assuming a low Reynolds regime, the inertial forces can be neglected and, therefore, the fluid motion is modelled by the Stokes system. We first prove the well posedness of the corresponding system. Then we show an identifiability result: with one measure of the Cauchy forces of the fluid on one given part of the boundary and at some positive time, the shape of a convex body and its initial position are identified.

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Section: Resultsmentioning

confidence: 94%

“…Now, let us take two smooth non-empty domains S (1) 0 and S (2) 0 . Let us also consider a (1) 0 , Q (1) 0 , a (2) 0 , Q (2) 0 (1) 0 , Q (1) 0 ⊂ and S (2) a (2) 0 , Q (2) 0 ⊂ .…”

Section: Resultsmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 93%

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the identifiability of a rigid body moving in a stationary viscous fluid

Conca¹,

Schwindt²,

Takahashi³

2011

Inverse Problems

Self Cite

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The identification of obstacles immersed in a steady incompressible viscous fluid

Yuksel,

Lesnic

2024

J Eng Math

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In this paper, the identification of immersed obstacles in a steady incompressible Navier-Stokes viscous fluid flow from fluid traction measurements is investigated. The solution of the direct problem is computed using the finite element method (FEM) implemented in the Freefem++ commercial software package. The solution of the inverse geometric obstacle problem (parameterized by a small set of unknown constants) is accomplished iteratively by minimizing the nonlinear least-squares functional using an adaptive moment estimation algorithm. The numerical results for the identification of an obstacle in a viscous fluid flowing in a channel with open ends, show that when the fluid traction is measured on the top, bottom and inlet boundaries, then the algorithm provides accurate and robust reconstructions of an obstacle parameterized by a small number of parameters in a Fourier trigonometric finite expansion. Stable reconstructions with respect to noise in the measured fluid traction data are also achieved, although for complicated shapes parameterized by larger degrees of freedom nonlinear Tikhonov regularization of the least-squares functional may need to be employed. Multiple-component obstacles may also be identified provided that a good initial guess is provided. In case of limited data being available only at the inlet boundary the pressure gradient provides more information for inversion than the fluid traction.

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