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In this work three branches of Immersed Boundary Methods (IBM) are described and validated for incompressible aerodynamics and fluid-structure interactions. These three approaches are: Cut Cell method, Vortex-Penalization method and Forcing method. The first two techniques are validated for external bluff-body flow around a circular obstacle. The last one is used to predict the deformations of an elastic membrane immersed in a fluid. The paper confirms the ability of this family of numerical schemes...
On établit ici, suivant [5], une inégalité de Carleman globale optimale pour les solutions faibles (au sens ) d’équations elliptiques générales avec second membre dans et trace non nulle.La motivation, qui est expliquée dans l’introduction, réside dans l’obtention d’inégalités de Carleman globale pour l’opérateur de Navier-Stokes linéarisé afin, notamment, d’étudier les questions de contrôlabilité exacte sur les trajectoires pour les équations de Navier-Stokes. Une étape majeure consiste à obtenir...
In this paper we establish interior regularity for weak solutions and partial regularity for suitable weak solutions of the perturbed Navier-Stokes system, which can be regarded as generalizations of the results in L. Caffarelli, R. Kohn, L. Nirenberg: Partial regularity of suitable weak solutions of the Navier-Stokes equations, Commun. Pure. Appl. Math. 35 (1982), 771–831, and S. Takahashi, On interior regularity criteria for weak solutions of the Navier-Stokes equations, Manuscr. Math. 69...
We investigate the existence, uniqueness and polynomial stability of the weighted pseudo almost automorphic solutions to a class of linear and semilinear parabolic evolution equations. The necessary tools here are interpolation spaces and interpolation theorems which help to prove the boundedness of solution operators in appropriate spaces for linear equations. Then for the semilinear equations the fixed point arguments are used to obtain the existence and stability of the weighted pseudo almost...
The aim of this talk is to present recent results obtained with N. Masmoudi on the free surface Navier-Stokes equations with small viscosity.
The article is devoted to the simulation of viscous incompressible fluid flow based on solving the Navier-Stokes equations. As a numerical model we chose isogeometrical approach. Primary goal of using isogemetric analysis is to be always geometrically exact, independently of the discretization, and to avoid a time-consuming generation of meshes of computational domains. For higher Reynolds numbers, we use stabilization techniques SUPG and PSPG. All methods mentioned in the paper are demonstrated...
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