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Non reflecting boundary conditions on artificial frontiers
of the domain are proposed for both
incompressible and compressible Navier-Stokes equations.
For incompressible flows, the boundary conditions lead to a well-posed
problem, convey properly the vortices without any reflections on the
artificial limits and allow to compute turbulent flows at high Reynolds
numbers.
For compressible flows, the boundary conditions convey properly the
vortices without any reflections on the artificial limits...
We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded, for which the worst-case in terms of recirculation effects is inferred to correspond to a strong orifice flow through near-complete occlusion.A worst-case optimal control approach is applied to the steady Navier-Stokes...
Ω being a bounded open set in R∙, with regular boundary, we associate with Navier-Stokes equation in Ω where the velocity is null on ∂Ω, a non-linear branching process (Yt, t ≥ 0). More precisely: Eω0(〈h,Yt〉) = 〈ω,h〉, for any test function h, where ω = rot u, u denotes the velocity solution of Navier-Stokes equation. The support of the random measure Yt increases or decreases in one unit when the underlying process hits ∂Ω; this stochastic phenomenon corresponds to the creation-annihilation of vortex...
In this work we introduce a new class of lowest order methods for diffusive problems on general meshes with only one unknown per element. The underlying idea is to construct an incomplete piecewise affine polynomial space with optimal approximation properties starting from values at cell centers. To do so we borrow ideas from multi-point finite volume methods, although we use them in a rather different context. The incomplete polynomial space replaces classical complete polynomial spaces in discrete...
In this work we introduce a new class of lowest order methods for
diffusive problems on general meshes with only one unknown per
element.
The underlying idea is to construct an incomplete piecewise affine
polynomial space with optimal approximation properties starting
from values at cell centers.
To do so we borrow ideas from multi-point finite volume methods,
although we use them in a rather different context.
The incomplete polynomial space replaces classical complete
polynomial spaces...
Nous montrons dans cette étude l’existence de configurations stationnaires où une bille tombe le long d’un plan incliné sans le toucher. Nous donnons également des propriétés qualitatives de ces configurations. En particulier, nous nous intéressons à l’orientation du plan par rapport à la verticale quand la masse de la bille est proche de celle d’un volume équivalent de liquide i.e., quand l’écoulement autour de la bille est lent.
We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force in the close-contact limit. In this way, we recover and clarify the various expressions that can be found in previous studies.
We consider the effect of surface roughness on solid-solid contact in a Stokes flow.
Various models for the roughness are considered, and a unified methodology is given to
derive the corresponding asymptotics of the drag force in the close-contact limit. In this
way, we recover and clarify the various expressions that can be found in previous
studies.
We consider the effect of surface roughness on solid-solid contact in a Stokes flow.
Various models for the roughness are considered, and a unified methodology is given to
derive the corresponding asymptotics of the drag force in the close-contact limit. In this
way, we recover and clarify the various expressions that can be found in previous
studies.
We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac-like inequalities. As part of our methods, we give a different approach to a priori estimates of Foiaş, Guillopé and Temam.
In the context of suitable weak solutions to the Navier-Stokes equations we present local conditions of Prodi-Serrin’s type on velocity and pressure under which is a regular point of . The conditions are imposed exclusively on the outside of a sufficiently narrow space-time paraboloid with the vertex and the axis parallel with the -axis.
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