Motion of a rigid body in a compressible fluid with Navier-slip boundary condition

Nečasová, Šárka; Ramaswamy, Mythily; Roy, Arnab; Schlömerkemper, Anja

doi:10.1016/j.jde.2022.07.045

Cited by 8 publications

(3 citation statements)

References 26 publications

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“…Moreover, in the L p − L q setting, the compressible problem in a moving domain is studied in [50]. In [62], the existence of a weak solution to fluid-solid interaction problem is proved considering slip boundary conditions.…”

Section: Introduction and Main Resultmentioning

confidence: 99%

Existence of strong solutions for a compressible fluid-solid interaction system with Navier slip boundary conditions

Djebour

2024

EECT

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We consider a fluid-structure interaction system coupling a viscous fluid governed by the compressible Navier-Stokes equations and a rigid body immersed in the fluid and modeled by the Newton's law. In this work, we consider the Navier slip boundary conditions. Our aim is to show the local in time existence and uniqueness of the strong solution to the corresponding problem. The main step of this work is that we use Lagrangian change of variables in order to handle the transport equation and to reduce the problem in the initial domain. However, the specificity here is that the Lagrangian coordinates do not coincide with the Eulerian coordinates at the boundaries since we consider slip boundary conditions. Therefore, it brings some extra nonlinear terms in the boundary conditions. The strategy is based on the study of the linearized system with nonhomogeneous boundary conditions and on the Banach fixed point theorem.

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Section: Introduction and Main Resultmentioning

confidence: 99%

Existence of strong solutions for a compressible fluid-solid interaction system with Navier slip boundary conditions

Djebour

2024

EECT

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“…However in the past few years there have been works exploring the fluid structure interaction problems comprising the compressible Navier-Stokes equations. For instance we refer to the articles [33,11,42,44,59] (rigid body immersed inside the fluid domain) and [10,46] (elastic structure inside the fluid). Further we quote the articles [53,56] (strong solutions with damped elastic structure), [6] (semigroup well posedness with an undamped structure) and [52] (strong solution with a wave equation) for the analysis of compressible fluid structure interaction models with the structure/ wave appearing at the fluid boundary.…”

Section: 3mentioning

confidence: 99%

Existence of weak solution for a compressible multicomponent fluid structure interaction problem

Kalousek¹,

Mitra²,

Nečasová³

2023

Preprint

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In this article, we analyze a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modelled by a system resembilng compressible Navier-Stokes equations with a physically realistic pressure depending on densities of both the fluids. In fact in the present article the dependence of the fluid pressure on the densities is analogous to the ones considered in [60] (where the authors deal with a bi-fluid system in a time independent smooth domain). The shell constitutes the boundary of the fluid domain and it possesses a non-linear, nonconvex Koiter energy (of a quite general form). We are interested in the existence of a weak solution to the system until the time-dependent boundary approaches a self-intersection or the Koiter energy degenerates. We first prove a global existence result (until a degeneracy occurs) when the adiabatic exponents solve max{γ, β} > 2 and min{γ, β} > 0, further the densities are comparable and the structure involved is non-dissipative. Next with the assumption that the structure is dissipative we extend our global existence result to the critical case max{γ, β} ≥ 2 and min{γ, β} > 0. The result is achieved in several steps involving, extension of the physical domain, penalization of the interface condition, artificial regularization of the shell energy, added structural dissipation and suitable limit passages depending on uniform estimates. In order to deal with the bi-fluid system we generalize the almost compactness argument developed in [60,68] to the case of time dependent domains with uniform Hölder continuous boundaries. Moreover, the proof of such a compactness result depends on the existence of renormalized continuity equation in time dependent domains.

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“…Moreover, the problem has been studied in the case of the Navier-slip instead of the classical no-slip boundary condition, cf. [37], and also the question about the existence of strong solutions has been investigated in both the compressible, cf. [3,30,31,40], and the incompressible case, cf.…”

Section: Introductionmentioning

confidence: 99%

Fluid–rigid body interaction in a compressible electrically conducting fluid

Scherz

2023

Mathematische Nachrichten

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We consider a system of multiple insulating rigid bodies moving inside of an electrically conducting compressible fluid. In this system, we take into account the interaction of the fluid with the bodies as well as with the electromagnetic fields trespassing both the fluid and the solids. The main result of this paper yields the existence of weak solutions to the system. While the mechanical part of the problem can be dealt with via a classical penalization method, the electromagnetic part requires an approximation by means of a hybrid discrete–continuous in time system: The discrete part of the approximation enables us to handle the solution‐dependent test functions in our variational formulation of the induction equation, whereas the continuous part makes sure that the nonnegativity of the density and subsequently a meaningful energy inequality is preserved in the approximate system.

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Motion of a rigid body in a compressible fluid with Navier-slip boundary condition

Cited by 8 publications

References 26 publications

Existence of strong solutions for a compressible fluid-solid interaction system with Navier slip boundary conditions

Existence of strong solutions for a compressible fluid-solid interaction system with Navier slip boundary conditions

Existence of weak solution for a compressible multicomponent fluid structure interaction problem

Fluid–rigid body interaction in a compressible electrically conducting fluid

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