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spurious modes.

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Finite element analysis of sloshing and hydroelastic vibrations under gravity
Alfredo Bermúdez, Rodolfo Rodríguez
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 33 / Issue 2 / March 1999

Published online by Cambridge University Press:

15 August 2002, pp. 305-327

Print publication:

March 1999
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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 wellas 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.

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Finite element analysis of sloshing and hydroelastic vibrations under gravity

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Finite element analysis of sloshing and hydroelastic vibrations under gravity