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Student Number 982201019
Author Yeh-Hang Kao(高業航)
Author's Email Address hidog.gao@msa.hinet.net
Statistics This thesis had been viewed 545 times. Download 121 times.
Department Mathematics
Year 2010
Semester 2
Degree Master
Type of Document Master's Thesis
Language English
Title Finite element approximations of a fluid-structure interaction problem
Date of Defense 2011-07-08
Page Count 50
Keyword
  • finite element method
  • fluid-structure interaction problem
  • Lame system
  • Navier-Stokes equations
  • stabilized finite element method
  • Stokes equations
  • Abstract In this thesis, we study the finite element approximations to a fluid-structure interaction problem that describes the viscous fluid flow interacting with an elastic structure by using the finite element package FreeFem++. We focus on the steady-state fluid-structure interaction problem in two dimensions. The fluid motion is governed by the viscous, incompressible Stokes or the Navier-Stokes equations, while the elastic solid is modeled by the Lame system of elasticity. We propose a direct iterative finite element algorithm to solve the coupling system, where the structure part is solved by the standard finite element method and the fluid part is solved by a stabilized finite element method. Numerical simulations of several examples are presented to illustrate the effectiveness of the proposed direct iterative finite element algorithm.
    Table of Content 目錄
    中文摘要........................................................... i
    英文摘要........................................................... ii
    目錄.............................................................. iii
    Abstract ........................................................................................................................ 1
    1. introduction ........................................................................................................... 2
    2. The elastic structure .............................................................................................. 5
    2.1. The Lame system of elasticity ........................................................................ 5
    2.2. Finite element method for the Lame system ................................................. 6
    2.3. Numerical example ........................................................................................ 7
    3. The viscous incompressible flows .......................................................................... 9
    3.1. The Stokes equations ..................................................................................... 9
    3.2. The stabilized finite element method for the Stokes equations .................... 9
    3.3. Numerical examples of the Stokes equations .............................................. 11
    3.4. The Navier-Stokes equations ....................................................................... 14
    3.5. An algorithm for solving the Navier-Stokes equations ................................ 14
    3.6. The stabilized finite element method for the linearized Navier-Stokes
    equations ........................................................................................................... 15
    3.7. Numerical examples of the Navier-Stokes equations .................................. 16
    4. The fluid-structure interaction problems ............................................................ 23
    4.1. The coupling problem of the Stokes equations with the Lame system ....... 23
    4.2. Numerical examples of the coupling problem of the Stokes equations with
    the Lame system................................................................................................ 24
    4.3. The coupling problem of the Navier-Stokes equations with the Lame
    system................................................................................................................ 29
    4.4. Numerical examples of tahe coupling problem of the Navier-Stokes
    equations with the Lame system ...................................................................... 30
    5. Summary and conclusions ................................................................................... 43
    References ................................................................................................................. 44
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    Methods in Applied Sciences and Engineering, July 24-28, 2004.
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    [13] J. Janela, A. Moura, and A. Sequeira, A 3D non-Newtonian °uid-structure interaction model
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    [15] R. Rannacher, Finite element methods for the incompressible Navier-Stokes equations,
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    Advisor
  • Suh-Yuh Yang(楊肅煜)
  • Files
  • 982201019.pdf
  • approve immediately
    Date of Submission 2011-07-12

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