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The Immersed Boundary Smooth Extensi...

Stein, David Bradley.

The Immersed Boundary Smooth Extension (IBSE) Method: A Flexible and Accurate Fictitious Domain Method, and Applications to the Study of Polymeric Flow in Complex Geometries.

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Immersed Boundary Smooth Extension (IBSE) Method: A Flexible and Accurate Fictitious Domain Method, and Applications to the Study of Polymeric Flow in Complex Geometries.
Author:	Stein, David Bradley.
Published:	Ann Arbor : ProQuest Dissertations & Theses, 2016
Description:	157 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.
Notes:	Adviser: Becca Thomases.
Contained By:	Dissertation Abstracts International78-03B(E).
Subject:	Applied mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10182828
ISBN:	9781369311433

The Immersed Boundary Smooth Extension (IBSE) Method: A Flexible and Accurate Fictitious Domain Method, and Applications to the Study of Polymeric Flow in Complex Geometries.
Stein, David Bradley.

The Immersed Boundary Smooth Extension (IBSE) Method: A Flexible and Accurate Fictitious Domain Method, and Applications to the Study of Polymeric Flow in Complex Geometries. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 157 p.

Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.

Thesis (Ph.D.)--University of California, Davis, 2016.

Embedded boundary methods are a large class of numerical schemes that allow the solution of partial differential equations set on complex geometries to be solved on simple domains using fast and robust techniques for discretizing partial differential equations on regular Cartesian meshes. One example is the Immersed Boundary (IB) method, which enforces boundary conditions on an interface by adding a regularized singular force distribution supported in a small neighborhood of the boundary. Although the IB method is fast, flexible, and has been shown to produce valid solutions to a variety of fluid-structure interaction problems, the solutions produced by the IB method have limited regularity and accuracy. In particular, components of the stress tensor fail to converge pointwise, with large errors near the interface. For polymeric flow problems, we demonstrate that the IB method fails to accurately capture the polymeric stress near to and on the boundary. To remedy this deficiency, we introduce a modification of the IB method designed to produce more accurate solutions that correctly capture the stress near the boundaries.

ISBN: 9781369311433Subjects--Topical Terms:

377601
Applied mathematics.

The Immersed Boundary Smooth Extension (IBSE) Method: A Flexible and Accurate Fictitious Domain Method, and Applications to the Study of Polymeric Flow in Complex Geometries.
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245 1 4 $a The Immersed Boundary Smooth Extension (IBSE) Method: A Flexible and Accurate Fictitious Domain Method, and Applications to the Study of Polymeric Flow in Complex Geometries.
260 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2016
300 $a 157 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.
500 $a Adviser: Becca Thomases.
502 $a Thesis (Ph.D.)--University of California, Davis, 2016.
520 $a Embedded boundary methods are a large class of numerical schemes that allow the solution of partial differential equations set on complex geometries to be solved on simple domains using fast and robust techniques for discretizing partial differential equations on regular Cartesian meshes. One example is the Immersed Boundary (IB) method, which enforces boundary conditions on an interface by adding a regularized singular force distribution supported in a small neighborhood of the boundary. Although the IB method is fast, flexible, and has been shown to produce valid solutions to a variety of fluid-structure interaction problems, the solutions produced by the IB method have limited regularity and accuracy. In particular, components of the stress tensor fail to converge pointwise, with large errors near the interface. For polymeric flow problems, we demonstrate that the IB method fails to accurately capture the polymeric stress near to and on the boundary. To remedy this deficiency, we introduce a modification of the IB method designed to produce more accurate solutions that correctly capture the stress near the boundaries.
520 $a The primary work of this dissertation is the introduction of the Immersed Boundary Smooth Extension (IBSE) method, which couples the solution of the underlying PDE with the smooth extension of that unknown solution to the entire domain. The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta-functions to communicate information between the computational grid and the boundary. Through a wide range of examples, including the Poisson, heat, Burgers, Fitzhugh-Nagumo, Stokes, Navier-Stokes, and Stokes-Oldroyd-B problems, we demonstrate that the IBSE method produces globally smooth solutions that converge rapidly, up to fourth-order in the grid spacing. For fluid problems, the IBSE method provides pointwise converge of all elements of the stress tensor. We conclude by demonstrating accurate solutions to a challenging benchmark problem for polymeric fluids: the flow of a Stokes-Oldroyd-B fluid around a cylinder in a confined channel.
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