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On the Advective Component of Active Flux Schemes for Nonlinear Hyperbolic Conservation Laws.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	On the Advective Component of Active Flux Schemes for Nonlinear Hyperbolic Conservation Laws./
Author:	Maeng, Jungyeoul Brad.
Description:	1 online resource (249 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.
Subject:	Aerospace engineering. -
Online resource:	click for full text (PQDT)
ISBN:	9780355366099

On the Advective Component of Active Flux Schemes for Nonlinear Hyperbolic Conservation Laws.
Maeng, Jungyeoul Brad.

On the Advective Component of Active Flux Schemes for Nonlinear Hyperbolic Conservation Laws. - 1 online resource (249 pages)

Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.

Thesis (Ph.D.)--University of Michigan, 2017.

Includes bibliographical references

A new class of numerical methods called Active Flux (AF) is investigated for nonlinear hyperbolic conservation laws. The AF method is designed specifically to address the aspect that most modern compressible flow methods fail to do; the multidimensionality aspect. It addresses the shortcoming by employing a two stage update process. In the first stage, a nonconservative form of the system is introduced to provide the flexibility to pursue distinct numerical approaches for flow processes with differing physics. Because each process is treated separately, the numerical method can be appropriately formed to reflect each type of physics and to provide the maximal stability. The method is completed with the conservation update to produce a third-order accurate scheme.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355366099Subjects--Topical Terms:

686400
Aerospace engineering.
Index Terms--Genre/Form:

554714
Electronic books.

On the Advective Component of Active Flux Schemes for Nonlinear Hyperbolic Conservation Laws.
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245 1 0 $a On the Advective Component of Active Flux Schemes for Nonlinear Hyperbolic Conservation Laws.
264 0 $c 2017
300 $a 1 online resource (249 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.
500 $a Adviser: Philip L Roe.
502 $a Thesis (Ph.D.)--University of Michigan, 2017.
504 $a Includes bibliographical references
520 $a A new class of numerical methods called Active Flux (AF) is investigated for nonlinear hyperbolic conservation laws. The AF method is designed specifically to address the aspect that most modern compressible flow methods fail to do; the multidimensionality aspect. It addresses the shortcoming by employing a two stage update process. In the first stage, a nonconservative form of the system is introduced to provide the flexibility to pursue distinct numerical approaches for flow processes with differing physics. Because each process is treated separately, the numerical method can be appropriately formed to reflect each type of physics and to provide the maximal stability. The method is completed with the conservation update to produce a third-order accurate scheme.
520 $a The AF advection scheme is founded on the characteristic tracing method, a semi-Lagrangian method, which has long been used for developing numerical methods for hyperbolic problems. The first known AF method for advection, Scheme V by van Leer, is revisited as a part of the development of the scheme. Details of Scheme V are examined closely, and new improvements are made for the multidimensional nonlinear advection scheme.
520 $a A detailed study of the nonlinear system of equations is made possible by the pressureless Euler system, which is the advective component of the Euler system. It serves as a stepping stone for the Euler system, and all necessary details of the nonlinear system are explored. Lastly, an extension to the Euler system is presented where a novel nonlinear operator splitting method is introduced to correctly blend the contributions of the nonlinear advection and acoustic processes. The AF method, as a result, produces a maximally stable, third-order accurate method for the multidimensional Euler system.
520 $a Some guiding principles of limiting are presented. Because two types of flow feature are separately treated, the limiting process must also be kept separate. Advective problems obeying natural bounding principles are treated differently from acoustic problems with no explicit bounding principles. Distinct limiting approaches are explored along with discussions.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Aerospace engineering. $3 686400
655 7 $a Electronic books. $2 local $3 554714
690 $a 0538
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Michigan. $b Aerospace Engineering. $3 1179282
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10670355 $z click for full text (PQDT)