2026-09-19T22:33:25Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/578832022-01-13T07:54:11Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Mark Drela.
Kim, Jae Hyung, Ph. D. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
2010-08-31T16:20:58Z
2010-08-31T16:20:58Z
2010
2010
http://hdl.handle.net/1721.1/57883
639247283
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 93-94).
This thesis provides a numerical algorithm to solve fluid-structure interaction problems in the Cartesian grid. Unlike the typical Immersed Interfaced Method (IIM), we define thin non-stretchable solid interface with the Level Set function. In addition, we developed a partial differential equation which represents the bending rigidity of the interface. The interface is assumed very thin and has zero elastic stress when it is flat. The interface gives singular forces to the incompressible viscous fluid and the fluid solver handles discontinuities across the interface. Instead of solving two dynamic systems (i.e., fluid and solid), we solve the fluid field only and solve a convection equation of interface with the local fluid velocity. This idea is valid because of viscous fluid (i.e., velocity is continuous across the interface) as we can see frequently in the IIM. The result shows that elastic interface vibrates and converges to an equilibrium state. The oscillatory motion of the interface depends on the viscosity of fluid, Young's modulus and thickness of interface. The results looks correct physically, and they match with the existing IIM results.
by Jae Hyung Kim.
S.M.
94 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
copyright. They may be viewed from this source for any purpose, but
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http://dspace.mit.edu/handle/1721.1/7582
Aeronautics and Astronautics.
Simulation of thin elastic solids in the incompressible viscous flow using implicit interface representation
Thesis
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<Abstract>This thesis provides a numerical algorithm to solve fluid-structure interaction problems in the Cartesian grid. Unlike the typical Immersed Interfaced Method (IIM), we define thin non-stretchable solid interface with the Level Set function. In addition, we developed a partial differential equation which represents the bending rigidity of the interface. The interface is assumed very thin and has zero elastic stress when it is flat. The interface gives singular forces to the incompressible viscous fluid and the fluid solver handles discontinuities across the interface. Instead of solving two dynamic systems (i.e., fluid and solid), we solve the fluid field only and solve a convection equation of interface with the local fluid velocity. This idea is valid because of viscous fluid (i.e., velocity is continuous across the interface) as we can see frequently in the IIM. The result shows that elastic interface vibrates and converges to an equilibrium state. The oscillatory motion of the interface depends on the viscosity of fluid, Young's modulus and thickness of interface. The results looks correct physically, and they match with the existing IIM results.</Abstract>
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