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

Trifunović, Srđan; Wang, Ya-Guang

doi:10.48550/arxiv.2010.01639

Cited by 3 publications

(7 citation statements)

References 29 publications

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“…We consider a model where both the fluid and the structure conduct heat and there is heat coupling given through temperature continuity and entropy flux given in (1.26) and (1.28). While, in the context of fluid-structure interaction, heat-conducting fluids have been studied in [6] and thermoelastic structures have been studied in [56], to the best of our knowledge this is the first work that takes into account heat conduction of both components, and heat exchange between the components. One nice consequence of this approach is that we were able to prove that the plate temperature is non-negative which does not hold if one considers just a linear plate model without coupling it to the fluid with heat exchange.…”

Section: Main Results and Significancementioning

confidence: 99%

“…Recently, local-in-time existence results for strong solutions have been established for the compressible fluid-damped beam interaction in a 2D/1D framework in [44] and for the compressible fluid-undamped wave interaction in a 3D/2D framework in [41]. The existence of a weak solution was proven in [5,56] and in [4], a weak solution was obtained for an interaction problem between a compressible fluid and a 3D viscoelastic structure. To the best of our knowledge there are only a few very recent papers dealing with the mathematical analysis of FSI problems with a heat conducting fluid.…”

Section: Motivation and Literature Reviewmentioning

confidence: 99%

“…Remark 2.1. (1) The derivation of coupled momentum equation for smooth solutions is standard and we refer to [5,56] for more details. However, the coupled entropy inequality appears here for the first time and it is derived in Appendix B.…”

Section: The Energy Inequalitymentioning

confidence: 99%

“…Therefore, it is far from straightforward how to decouple the system and solve the fluid part separately. Here we use the decoupling method based on operator splitting from [56] (see also [47] where the splitting method in the context of FSI was introduced) which penalizes the fluid velocity and temperature to ensure the kinematic coupling conditions. More precisely, we split the time interval (0, T ) into subintervals of length ∆t.…”

Section: The Following Energy Inequalitymentioning

confidence: 99%

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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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Section: Main Results and Significancementioning

confidence: 99%

Section: Motivation and Literature Reviewmentioning

confidence: 99%

Section: The Energy Inequalitymentioning

confidence: 99%

Section: The Following Energy Inequalitymentioning

confidence: 99%

See 2 more Smart Citations

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

Mácha¹,

Muha²,

Nečasová³

et al. 2021

Preprint

Self Cite

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“…A similar foundational work in the compressible case is due to Lions [32] with important extensions by Feireisl et al [21,18]. Compressible fluids are important for applications in aero-dynamics and mathematical results on their interactions with elastic structures appeared in this context recently in [5,42]. A next natural step is to study the thermodynamics of fluid structure interactions.…”

Section: Introductionmentioning

confidence: 92%

Navier-Stokes-Fourier fluids interacting with elastic shells

Breit¹,

Schwarzacher²

2021

Preprint

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We study the motion of a compressible heat-conducting fluid in three dimensions interacting with a nonlinear flexible shell. The fluid is described by the full Navier-Stokes-Fourier system. The shell constitutes an unknown part of the boundary of the physical domain of the fluid and is changing in time. The solid is described as an elastic non-linear shell of Koiter type; in particular it possesses a non-convex elastic energy. We show the existence of a weak solution to the corresponding system of PDEs which exists until the moving boundary approaches a self-intersection or the non-linear elastic energy of the shell degenerates. It is achieved by compactness results (in highest order spaces) for the solid-deformation and fluid-density. Our solutions comply with the first and second law of thermodynamics: the total energy is preserved and the entropy balance is understood as a variational inequality. Contents 1. Introduction 1.1. State of art 1.2. The model 1.3. Mathematical strategy 1.4. Overview of the paper 2. Preliminaries 2.1. Structural and constitutive assumptions 2.2. Function spaces on variable domains 2.3. Extensions on variable domains 2.4. Convergence in variable domains. 2.5. Weak solutions and main theorem 3. Equations for density and temperature in variable domains 3.1. The continuity equation 3.2. The internal energy equation 4. Construction of an approximate solution 4.1. Galerkin approximation 4.2. Total energy balance 4.3. Compactness of ∂ t η N 4.4. Compactness of the shell energy 5. Construction of a solution. 5.1. The limit system for ε → 0 5.2. Compactness of the shell energy 5.3. Proof of Theorem 2.16. References

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Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation^*

2021

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In this article, we consider a fluid-structure interaction system where the fluid is viscous and compressible and where the structure is a part of the boundary of the fluid domain and is deformable. The fluid is governed by the barotropic compressible Navier-Stokes system, whereas the structure displacement is described by a wave equation. We show that the corresponding coupled system admits a unique, strong solution for an initial fluid density and an initial fluid velocity in H 3 and for an initial deformation and an initial deformation velocity in H 4 and H 3 respectively. The reference configuration for the fluid domain is a rectangular cuboid with the elastic structure being the top face. We use a modified Lagrangian change of variables to transform the moving fluid domain into the rectangular cuboid and then analyze the corresponding linear system coupling a transport equation (for the density), a heat-type equation, and a wave equation. The corresponding results for this linear system and estimations of the coefficients coming from the change of variables allow us to perform a fixed point argument and to prove the existence and uniqueness of strong solutions for the nonlinear system, locally in time.

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

Cited by 3 publications

References 29 publications

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

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

Navier-Stokes-Fourier fluids interacting with elastic shells

Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation^*

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

Cited by 3 publications

References 29 publications

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

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

Navier-Stokes-Fourier fluids interacting with elastic shells

Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation*

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Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation^*