New efficient boundary conditions for incompressible Navier-Stokes equations : a well-posedness result

Bruneau, Charles‐Henri; Fabrie, Pierre

doi:10.1051/m2an/1996300708151

Cited by 117 publications

(126 citation statements)

References 6 publications

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“…including (5.1) were proposed (for unsteady incompressible Navier-Stokes equations) in order to perform long-time simulations at high Reynolds numbers. See also [4], [5], [7]. Note that b 1 given by (5.1) meets (B1), (B2) with γ 1 = 3 and…”

Section: Boundary Conditions In Applicationsmentioning

confidence: 99%

On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

Lanzendörfer

Stebel

2011

Appl Math

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Section: Boundary Conditions In Applicationsmentioning

confidence: 99%

On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

Lanzendörfer

Stebel

2011

Appl Math

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“…Indeed, in that case, it is shown in [7,8] that such a model is well-posed and can be successfully used to compute flows in artificial domains without too much vortexes reflexions on Γ out and good agreement with the expected solution.…”

mentioning

confidence: 98%

“…Nevertheless in many cases the physical intuition of the behavior of the flow may help us to do so. As an example, for the classical computation of a flow past obstacles in an open channel, the Poiseuille reference flow is used in [6,7,8] and gives results that do not depend too much on the distance between the obstacles and the artificial open boundary of the computational domain. Furthermore, in the same references, numerical comparisons with the usual imposed normal stress condition are given showing that, for high Reynolds numbers, the nonlinear term in (2) is crucial to avoid non physical reflexions and blows up of the solution.…”

mentioning

confidence: 99%

Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations

Boyer¹,

Fabrie²

2007

Discrete &Amp; Continuous Dynamical Systems - B

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Abstract. In this paper we propose the analysis of the incompressible nonhomogeneous Navier-Stokes equations with nonlinear outflow boundary condition. This kind of boundary condition appears to be, in some situations, a useful way to perform numerical computations of the solution to the unsteady Navier-Stokes equations when the Dirichlet data are not given explicitly by the physical context on a part of the boundary of the computational domain.The boundary condition we propose, following previous works in the homogeneous case, is a relationship between the normal component of the stress and the outflow momentum flux taking into account inertial effects. We prove the global existence of a weak solution to this model both in 2D and 3D. In particular, we show that the nonlinear boundary condition under study holds for such a solution in a weak sense, even though the normal component of the stress and the density may not have traces in the usual sense.

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“…We made a few attempts with Dirichlet conditions, taking into account the corresponding compatibility conditions for the Stokes equation; however they produce irrelevant velocity profiles next to the boundary. Possible improvements of the condition can also be found in [2][3][4].…”

Section: Boundary Conditions Formentioning

confidence: 97%

A mixture model for the dynamic of the gut mucus layer

Bouti¹,

Goudon

Labarthe

et al. 2016

ESAIM: ProcS

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Abstract. We introduce a mixture model intended to describe the dynamics of the mucus layer that wraps the gut mucosa. This model takes into account the fluid mechanics of the gut content, the inhomogeneous rheology that depends on the fluid composition, and the main physiological mechanisms that ensure the homoeostasis of the mucus layer. Numerical simulations, based on a finite volume approach, prove the ability of the model to produce a stable steady-state mucus layer. We also perform a sensitivity analysis by using a meta-model based on polynomial chaos in order to identify the main parameters impacting the shape of the mucus layer. The effect of the interaction of the mucus with a population of bacteria is eventually discussed.Résumé. Nous présentons un modèle de mélange qui décrit l'évolution de la couche de mucus qui recouvre la muqueuse du gros intestin. Ce modèle prend en compte la mécanique des fluides qui composent le contenu intestinal, la rhéologie inhomogène dépendant de la composition du fluide et les principaux mécanismes physiologiques qui assurent l'homéostasie de la couche de mucus. Des résultats numériques, obtenus par une méthode volumes finis, démontrent la capacité du modèleà reproduire une couche de mucus stationnaire stable. Nous pratiquons ensuite une analyse de sensibilité en construisant un métamodèle basé sur des polynômes de chaos afin d'identifier les paramètres impactant le plus la forme de la couche de mucus. Finalement, nous discutons les effets des interactions entre la couche de mucus et une population bactérienne chimiotactique.

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New efficient boundary conditions for incompressible Navier-Stokes equations : a well-posedness result

Cited by 117 publications

References 6 publications

On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations

A mixture model for the dynamic of the gut mucus layer

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