Finite element analysis of sloshing and hydroelastic vibrations under gravity

Bermúdez, Alfredo, and Rodríguez, Rodolfo. "Finite element analysis of sloshing and hydroelastic vibrations under gravity." ESAIM: Mathematical Modelling and Numerical Analysis 33.2 (2010): 305-327. <http://eudml.org/doc/197598>.

@article{Bermúdez2010,
abstract = { 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 linear eigenvalue problem. Lowest order triangular Raviart-Thomas elements are used for the fluid and classical piecewise linear elements for the solid. Transmission conditions at the fluid-solid interface are taken into account in a weak sense yielding a non conforming discretization. The method does not present spurious or circulation modes for nonzero frequencies. Convergence is proved and optimal error estimates are given. Finally, numerical results are shown. },
author = {Bermúdez, Alfredo, Rodríguez, Rodolfo},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Fluid-structure; finite elements; hydroelasticity under gravity; vibrations; spectral problems; spurious modes.; gravity effects; spurious modes; finite element method; fluid-structure interaction problems; harmonic hydroelastic vibrations; displacement formulation; well-posed mixed linear eigenvalue problem; triangular Raviart-Thomas elements; piecewise linear elements; fluid-solid interface; non-conforming discretization; convergence; optimal error estimates},
language = {eng},
month = {3},
number = {2},
pages = {305-327},
publisher = {EDP Sciences},
title = {Finite element analysis of sloshing and hydroelastic vibrations under gravity},
url = {http://eudml.org/doc/197598},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Bermúdez, Alfredo
AU - Rodríguez, Rodolfo
TI - Finite element analysis of sloshing and hydroelastic vibrations under gravity
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 2
SP - 305
EP - 327
AB - 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 linear eigenvalue problem. Lowest order triangular Raviart-Thomas elements are used for the fluid and classical piecewise linear elements for the solid. Transmission conditions at the fluid-solid interface are taken into account in a weak sense yielding a non conforming discretization. The method does not present spurious or circulation modes for nonzero frequencies. Convergence is proved and optimal error estimates are given. Finally, numerical results are shown.
LA - eng
KW - Fluid-structure; finite elements; hydroelasticity under gravity; vibrations; spectral problems; spurious modes.; gravity effects; spurious modes; finite element method; fluid-structure interaction problems; harmonic hydroelastic vibrations; displacement formulation; well-posed mixed linear eigenvalue problem; triangular Raviart-Thomas elements; piecewise linear elements; fluid-solid interface; non-conforming discretization; convergence; optimal error estimates
UR - http://eudml.org/doc/197598
ER -