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Theses

Analyse des équations modélisant le mouvement des systèmes couplant des solides rigides et des fluides visqueux

Abstract : In this thesis, we study the interaction between a viscous fluid and a rigid body. The latter is completely surrounded by the fluid and is subject to contact forces which are written with the Cauchy tensor. The classical Navier-Stokes equations are used to model the motion of the fluid. In addition to the inherent difficulties in these equations, we have, moreover, to deal with them in a variable domain which depends on the motion of the rigig body and thus, on the solution. We have showed existence and uniqueness of strong solutions of this system when the domain of the fluid is either bounded or the exterior of the rigid body. In both cases, the problem was studied in the two dimensional and three dimensional cases. In the case when the system fluid-rigid body is enclosed in a bounded domain, the existence was proved provided there is no contact between the rigid body and the boundary. We have also been interested in the approximation of the equations modelling the motion of the system. Fisrt, we have discretized in time our problem and we have proved, under some conditions, the convergence of the scheme. We have then discretized completely the system by using finite elements on a fixed mesh. This method is illustrated by some numerical tests.
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Theses
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http://docnum.univ-lorraine.fr/prive/SCD_T_2002_0270_TAKAHASHI.pdf
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https://hal.univ-lorraine.fr/tel-01746747
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Submitted on : Thursday, March 29, 2018 - 10:44:01 AM
Last modification on : Tuesday, March 2, 2021 - 5:12:06 PM

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  • HAL Id : tel-01746747, version 1

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Takéo Takahashi. Analyse des équations modélisant le mouvement des systèmes couplant des solides rigides et des fluides visqueux. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2002. Français. ⟨NNT : 2002NAN10270⟩. ⟨tel-01746747⟩

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