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Unconditionally Stable CutFEM for Dynamic Interfaces in a Fluid Structure Interaction Problem Sarkis, Marcus
Description
Interface problems arise in several applications including heart models, cochlea models, aquatic animal locomotion, blood cell motion, front-tracking in porous media flows and material science, to name a few. One of the difficulties in these problems is that solutions are normally not smooth across interfaces, and therefore standard numerical methods will lose accuracy near the interface unless the meshes align to it. However, it is advantageous to have meshes that do not align with the interface, especially for time dependent problems where the interface moves with time. Remeshing at every time step can be prohibitively costly, can destroy the structure of the mesh, or can deteriorate the well-conditioning of the stiffness matrix, and affect the stability of the problem. For a simple moving interface fluid-membrane interaction, we present a formal second-order finite element discretization in space and first-order in time where the finite element triangulation does not fit the interface and it is unconditionally stable in time independently of mesh parameters and fluid viscosity and membrane stiffness. This is a joint work with Kyle Dunn and Roger Lui from WPI.
Item Metadata
Title |
Unconditionally Stable CutFEM for Dynamic Interfaces in a Fluid Structure Interaction Problem
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-07-31T09:45
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Description |
Interface problems arise in several applications including
heart models, cochlea models, aquatic animal locomotion, blood cell motion,
front-tracking in porous media flows and material science, to name a few. One
of the difficulties in these problems is that solutions are normally not
smooth across interfaces, and therefore standard numerical methods will
lose accuracy near the interface unless the meshes align to it. However, it
is advantageous to have meshes that do not align with the interface,
especially for time dependent problems where the interface moves
with time. Remeshing at every time step can be prohibitively costly, can
destroy the structure of the mesh, or can deteriorate the well-conditioning of
the stiffness matrix, and affect the stability of the problem. For a
simple moving interface fluid-membrane interaction, we present a formal
second-order finite element discretization in space and first-order in time
where the finite element triangulation does not fit the interface and
it is unconditionally stable in time independently of mesh parameters and
fluid viscosity and membrane stiffness. This is a joint work with
Kyle Dunn and Roger Lui from WPI.
|
Extent |
37.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Mathematical Sciences Department - Worcester Polytechnic Institute
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Series | |
Date Available |
2019-03-17
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0377018
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International