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The Potential Exterior to Close-to-T...

Tao, Yuan.

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The Potential Exterior to Close-to-Touching Discs.

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Potential Exterior to Close-to-Touching Discs./
Author:	Tao, Yuan.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	91 p.
Notes:	Source: Dissertations Abstracts International, Volume: 80-08, Section: B.
Contained By:	Dissertations Abstracts International80-08B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13425833
ISBN:	9780438819429

The Potential Exterior to Close-to-Touching Discs.
Tao, Yuan.

The Potential Exterior to Close-to-Touching Discs. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 91 p.

Source: Dissertations Abstracts International, Volume: 80-08, Section: B.

Thesis (Ph.D.)--The University of Arizona, 2019.

This item must not be sold to any third party vendors.

There are many two-dimensional physical systems governed by potentials that satisfy the Laplace's equation and Dirichlet boundary condition. An elegant approach is to set up the problem in the complex plane and use the freedom of conformal mappings to map the region and equation to different domains. In this paper, I focus on the problem of a uniform flow past two close-to-touching discs and the goal is to determine the potential and velocity field. The problem becomes very singular if the separation of the two discs gets smaller and it poses a challenge to both numerical and analytical solutions. Numerically, we come up with a new method that combines the method of images with conformal mappings and it performs better than all existing numerical methods in terms of efficiency and robustness. Analytically, we have a "limit solution" that matches the true solution uniformly and the "limit solution" is more accurate when the discs are closer. This solution also gives explicit relations between the behavior of the flow and the separation of the two discs.

ISBN: 9780438819429Subjects--Topical Terms:

1669109
Applied Mathematics.
Subjects--Index Terms:

Dirichlet boundary

The Potential Exterior to Close-to-Touching Discs.
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020 $a 9780438819429
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100 1 $a Tao, Yuan. $3 3545162
245 1 4 $a The Potential Exterior to Close-to-Touching Discs.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 91 p.
500 $a Source: Dissertations Abstracts International, Volume: 80-08, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Venkataramani, Shankar C.
502 $a Thesis (Ph.D.)--The University of Arizona, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a There are many two-dimensional physical systems governed by potentials that satisfy the Laplace's equation and Dirichlet boundary condition. An elegant approach is to set up the problem in the complex plane and use the freedom of conformal mappings to map the region and equation to different domains. In this paper, I focus on the problem of a uniform flow past two close-to-touching discs and the goal is to determine the potential and velocity field. The problem becomes very singular if the separation of the two discs gets smaller and it poses a challenge to both numerical and analytical solutions. Numerically, we come up with a new method that combines the method of images with conformal mappings and it performs better than all existing numerical methods in terms of efficiency and robustness. Analytically, we have a "limit solution" that matches the true solution uniformly and the "limit solution" is more accurate when the discs are closer. This solution also gives explicit relations between the behavior of the flow and the separation of the two discs.
590 $a School code: 0009.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Mathematics. $3 515831
653 $a Dirichlet boundary
653 $a Laplace's equation
653 $a Two-dimensional physical systems
690 $a 0364
690 $a 0405
710 2 $a The University of Arizona. $b Mathematics. $3 1032088
773 0 $t Dissertations Abstracts International $g 80-08B.
790 $a 0009
791 $a Ph.D.
792 $a 2019
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13425833