An $hp$ Finite Element Method to Solve a Fluid-Solid Vibration Problem

This paper deals with a two-dimensional fluid-solid vibration problem arising from nuclear engineering: the vibration of elastically mounted tubes immersed in a cavity filled with fluid. A convenient variational formulation of this problem, valid for compressible and incompressible fluids, is introd...

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Bibliographic Details
Published in:SIAM journal on scientific computing Vol. 34; no. 5; pp. A2533 - A2557
Main Authors: Padra, Claudio, Rodríguez, Rodolfo, Scheble, Mario
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2012
Subjects:
Approximation
Eigenvalues
Finite element analysis
Nuclear engineering
Velocity
ISSN:1064-8275, 1095-7197
Online Access:Get full text
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Summary:This paper deals with a two-dimensional fluid-solid vibration problem arising from nuclear engineering: the vibration of elastically mounted tubes immersed in a cavity filled with fluid. A convenient variational formulation of this problem, valid for compressible and incompressible fluids, is introduced. An $hp$ finite element method is used for its discretization, which leads to a well posed matrix eigenvalue problem. Optimal order a priori error estimates are proved for eigenfunctions and eigenvalues. Then, local a posteriori error indicators are defined and its efficiency and reliability are studied. An adaptive scheme driven by these indicators is proposed and numerically tested. [PUBLICATION ABSTRACT]
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ISSN:1064-8275
1095-7197
DOI:10.1137/120868396