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Navier-Stokes Equations in One and Two Dimensions.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Navier-Stokes Equations in One and Two Dimensions./
Author:	Nerdal, Jon.
Description:	1 online resource (51 pages)
Notes:	Source: Masters Abstracts International, Volume: 84-04.
Contained By:	Masters Abstracts International84-04.
Subject:	Numerical analysis. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29402902click for full text (PQDT)
ISBN:	9798352649039

Navier-Stokes Equations in One and Two Dimensions.
Nerdal, Jon.

Navier-Stokes Equations in One and Two Dimensions. - 1 online resource (51 pages)

Source: Masters Abstracts International, Volume: 84-04.

Thesis (Ph.D.)--Louisiana State University and Agricultural & Mechanical College, 2022.

Includes bibliographical references

The Navier-Stokes equations are an important tool in understanding and describing fluid flow. We investigate different formulations of the incompressible Navier-Stokes equations in the one-dimensional case along an axis and in the two-dimensional case in a circular pipe without swirl. For the one-dimensional case we show that the velocity approximations are remarkably accurate and we suggest that understanding this simple axial behaviour is an important starting point for further exploration in higher dimensions. The complexity of the boundary is then increased with the two-dimensional case of fluid flow through the cross section of a circular pipe, where we investigate two separate formulations of the Navier-Stokes equations and observe their differences. The first twodimensional formulation exhibits an auxiliary field which differs from the velocity by a gauge transformation. We are then able to eliminate the ambiguity related to the pressure boundary condition in the traditional formulation since the gauge freedom lets us assign specific and simple boundary conditions for both the auxiliary field and the gauge field. The latter two-dimensional formulation considers external forces acting on the fluid and resembles a more traditional approach to solving the Navier-Stokes equations. The two-dimensional results are then discussed and found to correspond with fluid mechanics theory given the initial conditions as well as the boundary conditions of the systems.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798352649039Subjects--Topical Terms:

517751
Numerical analysis.
Index Terms--Genre/Form:

542853
Electronic books.

Navier-Stokes Equations in One and Two Dimensions.
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100 1 $a Nerdal, Jon. $3 3695168
245 1 0 $a Navier-Stokes Equations in One and Two Dimensions.
264 0 $c 2022
300 $a 1 online resource (51 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Masters Abstracts International, Volume: 84-04.
500 $a Advisor: Olafsson, Gestur.
502 $a Thesis (Ph.D.)--Louisiana State University and Agricultural & Mechanical College, 2022.
504 $a Includes bibliographical references
520 $a The Navier-Stokes equations are an important tool in understanding and describing fluid flow. We investigate different formulations of the incompressible Navier-Stokes equations in the one-dimensional case along an axis and in the two-dimensional case in a circular pipe without swirl. For the one-dimensional case we show that the velocity approximations are remarkably accurate and we suggest that understanding this simple axial behaviour is an important starting point for further exploration in higher dimensions. The complexity of the boundary is then increased with the two-dimensional case of fluid flow through the cross section of a circular pipe, where we investigate two separate formulations of the Navier-Stokes equations and observe their differences. The first twodimensional formulation exhibits an auxiliary field which differs from the velocity by a gauge transformation. We are then able to eliminate the ambiguity related to the pressure boundary condition in the traditional formulation since the gauge freedom lets us assign specific and simple boundary conditions for both the auxiliary field and the gauge field. The latter two-dimensional formulation considers external forces acting on the fluid and resembles a more traditional approach to solving the Navier-Stokes equations. The two-dimensional results are then discussed and found to correspond with fluid mechanics theory given the initial conditions as well as the boundary conditions of the systems.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Numerical analysis. $3 517751
650 4 $a Fluids. $3 790092
650 4 $a Partial differential equations. $3 2180177
650 4 $a Viscosity. $3 1050706
650 4 $a Boundary conditions. $3 3560411
650 4 $a Navier-Stokes equations. $3 628091
650 4 $a Applied mathematics. $3 2122814
650 4 $a Mathematics. $3 515831
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0364
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a Louisiana State University and Agricultural & Mechanical College. $3 783779
773 0 $t Masters Abstracts International $g 84-04.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29402902 $z click for full text (PQDT)