On an existence theory for a fluid-beam problem encompassing possible contacts

Casanova, Jean-Jérôme; Grandmont, Céline; Hillairet, Matthieu

doi:10.5802/jep.162

Cited by 15 publications

(6 citation statements)

References 14 publications

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“…Thus, the authors construct a weak solution based on the time semi-discretization and operator splitting approach for this problem, under certain assumptions for the approximate shell displacement which ensure that it is regular enough and doesn't self-intersect on some time interval. In [8], global weak solutions for 2D interaction problem between an incompressible viscous fluid and an elastic beam with possible contact were constructed, as a limit of a sequence of strong global solutions constructed in [23] as viscoelasticity coefficient goes to zero. However, the contact mechanism was not prescribed.…”

Section: Introductionmentioning

confidence: 99%

On the interaction problem between a compressible viscous fluid and a nonlinear thermoelastic plate

Trifunović,

Wang

2020

Preprint

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In this paper we study the interaction problem between a nonlinear thermoelastic plate and a compressible viscous fluid with the adiabatic constant γ > 12/7. The existence of a weak solution for this problem is obtained by constructing a time-continuous operator splitting scheme that decouples the fluid and the structure. The fluid sub-problem is given on a fixed reference domain in the arbitrary Lagrangian-Eulerian (ALE) formulation, and the continuity equation is damped on this domain as well. This allows the majority of the analysis to be performed on the fixed reference domain, while the convergence of the approximate pressure is obtained on the physical domain.

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Section: Introductionmentioning

confidence: 99%

On the interaction problem between a compressible viscous fluid and a nonlinear thermoelastic plate

Trifunović,

Wang

2020

Preprint

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“…The question of how to analyse contact in the fluid-structure interaction is still largely open (see e.g. [26,20,19,7,27,24,58] and reference within) and is outside of the scope of this paper.…”

Section: The Problem Geometrymentioning

confidence: 99%

“…This is the point where we need strict positivity of ζ 7. This relation is not optimal, but it is enough to pass to the limit.…”

mentioning

confidence: 99%

Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange

Mácha¹,

Muha²,

Nečasová³

et al. 2021

Preprint

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In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heat-conducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a time-dependent domain which is filled with a fluid governed by the full Navier-Stokes-Fourier system. The fluid and the shell are fully coupled, giving rise to a novel nonlinear moving boundary fluidstructure interaction problem involving heat exchange. The existence of a weak solution is obtained by combining three approximation techniques -decoupling, penalization and domain extension. This approximation scheme allows us to use the methods already developed for fluids on moving domains, thus drastically simplifying the analysis at hand.

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“…2001; Joseph 2003 and the references therein). Moreover, some notions of weak solutions that allow for possible collisions have been considered by several authors (see, for example, Feireisl 2004; Casanova, Grandmont & Hillairet 2021).…”

Section: Introductionmentioning

confidence: 99%

Contactless rebound of elastic bodies in a viscous incompressible fluid

et al. 2022

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In this paper, we investigate the phenomenon of particle rebound in a viscous incompressible fluid environment. We focus on the important case of no-slip boundary conditions, where it is now well established that collisions cannot occur in finite time under certain assumptions. In a simplified framework, we provide conditions which allow us to prove that rebound is possible even in the absence of a topological contact. Our results lead to the conjecture that a qualitative change in the shape of the solid is necessary to obtain a physically meaningful rebound in fluids. We support the conjecture by comparing numerical simulations performed for the reduced model with finite element solutions obtained for corresponding well-established partial differential equation systems describing elastic solids interacting with incompressible fluids.

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On an existence theory for a fluid-beam problem encompassing possible contacts

Abstract: On an existence theory for a fluid-beam problem encompassing possible contacts Tome 8 (2021), p. 933-971.

Cited by 15 publications

References 14 publications

On the interaction problem between a compressible viscous fluid and a nonlinear thermoelastic plate

On the interaction problem between a compressible viscous fluid and a nonlinear thermoelastic plate

Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange

Contactless rebound of elastic bodies in a viscous incompressible fluid

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