Displaying similar documents to “Analysis of a coupled BEM/FEM eigensolver for the hydroelastic vibrations problem”

Automatic simplification of Darcy’s equations with pressure dependent permeability

Etienne Ahusborde, Mejdi Azaïez, Faker Ben Belgacem, Christine Bernardi (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We consider the flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with mixed boundary conditions. Since the boundary pressure can present high variations, the permeability of the medium also depends on the pressure, so that the model is nonlinear. estimates allow us to omit this dependence where the pressure does not vary too much. We perform the numerical analysis of a spectral element discretization of the simplified model. Finally we propose a strategy...

Finite element analysis of sloshing and hydroelastic vibrations under gravity

Alfredo Bermúdez, Rodolfo Rodríguez (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper deals with a finite element method to solve fluid-structure interaction problems. More precisely it concerns the numerical computation of harmonic hydroelastic vibrations under gravity. It is based on a displacement formulation for both the fluid and the solid. Gravity effects are included on the free surface of the fluid as well as on the liquid-solid interface. The pressure of the fluid is used as a variable for the theoretical analysis leading to a well posed mixed...

A priori error analysis of a fully-mixed finite element method for a two-dimensional fluid-solid interaction problem

Carolina Domínguez, Gabriel N. Gatica, Salim Meddahi, Ricardo Oyarzúa (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We introduce and analyze a fully-mixed finite element method for a fluid-solid interaction problem in 2D. The model consists of an elastic body which is subject to a given incident wave that travels in the fluid surrounding it. Actually, the fluid is supposed to occupy an annular region, and hence a Robin boundary condition imitating the behavior of the scattered field at infinity is imposed on its exterior boundary, which is located far from the obstacle. The media are governed by the...

Coupling Darcy and Stokes equations for porous media with cracks

Christine Bernardi, Frédéric Hecht, Olivier Pironneau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization...

Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements

Erwin Hernández (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We analyze an isoparametric finite element method to compute the vibration modes of a plate, modeled by Reissner-Mindlin equations, in contact with a compressible fluid, described in terms of displacement variables. To avoid locking in the plate, we consider a low-order method of the so called MITC (Mixed Interpolation of Tensorial Component) family on quadrilateral meshes. To avoid spurious modes in the fluid, we use a low-order hexahedral Raviart-Thomas elements and a non conforming...

A finite element method for stiffened plates

Ricardo Durán, Rodolfo Rodríguez, Frank Sanhueza (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The aim of this paper is to analyze a low order finite element method for a stiffened plate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beams equations. The resulting problem is shown to be well posed. In the case of concentric stiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysis and discretization of the first one is straightforward. The second one is shown to...