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Asymptotic and numerical analysis of...

Li, Lei.

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Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers./
作者:	Li, Lei.
面頁冊數:	138 p.
附註:	Source: Dissertation Abstracts International, Volume: 76-11(E), Section: B.
Contained By:	Dissertation Abstracts International76-11B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3712607
ISBN:	9781321895452

Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.
Li, Lei.

Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers. - 138 p.

Source: Dissertation Abstracts International, Volume: 76-11(E), Section: B.

Thesis (Ph.D.)--The University of Wisconsin - Madison, 2015.

Fluid-structure interaction is a big class of research topics and many are very active. We introduce several techniques for approaching some particular fluid-structure interaction problems and some research done by the author that is relevant to these methods. The governing equations for the fluid are the Navier-Stokes equations or their limit forms, namely the Stokes equations or the Euler equations. In different regimes, different tools are needed to approach the problems.

ISBN: 9781321895452Subjects--Topical Terms:

515831
Mathematics.

Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.
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245 1 0 $a Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.
300 $a 138 p.
500 $a Source: Dissertation Abstracts International, Volume: 76-11(E), Section: B.
500 $a Adviser: Saverio E. Spagnolie.
502 $a Thesis (Ph.D.)--The University of Wisconsin - Madison, 2015.
520 $a Fluid-structure interaction is a big class of research topics and many are very active. We introduce several techniques for approaching some particular fluid-structure interaction problems and some research done by the author that is relevant to these methods. The governing equations for the fluid are the Navier-Stokes equations or their limit forms, namely the Stokes equations or the Euler equations. In different regimes, different tools are needed to approach the problems.
520 $a We first introduce two techniques that are widely used in the study of Stokes flows (very viscous flows). The first is a slender body theory that takes advantage of the linearity of the Stokes equations and the small aspect ratio of the filament. The obtained asymptotic equation is a 1D partial differential equation about the dynamics of the centerline of the filament. We then use the slender body theory to approach the sedimentation of a weakly flexible filament. Taking advantage of the separation of time scales, we perform a multiple scale analysis to figure out the rotation rate and sedimentation velocity. Compared with a rigid rod, the weakly flexible filament reorients as it sediments and the lateral displacement is confined. The reorientation rate we derive is then used to explore the instability of a dilute suspension of weakly flexible filaments. The flexibility has double effects on the instability of the suspension: the flexibility creates a base state that renders more instability while the direct effect of the flexibility is to suppress the instability of the perturbation. The second is the boundary integral formulation for solving swimming and sedimentation problems of bodies, including non-slender ones, numerically. For the swimming problems of rigid helical bodies, we propose a boundary integral formulation by placing rotlets along the center line and introduce a special helical coordinate system for an asymptotic analysis method. The improved asymptotic results by a boundary layer analysis compare favorably with those computed using the boundary integral formulation.
520 $a Leaving the Stokes flows, we then look at the Eulerian immersed boundary method based on a local level set method, applicable at a more general Reynolds number. We propose a new level set method that involves two level set functions and a reinitialization process that preserves the interface gradient. The obtained Eulerian immersed boundary method is more stable compared with the traditional ones, with comparable costs. The limitation is that this method favors structures that have codimension one and needs further techniques in order to approach open structures (By "open", we mean the structures as manifolds have boundaries.).
520 $a To complete the story, we lastly introduce some classical complex analysis techniques for inviscid flows. We summarize Wu's derivation of the analytical results for a waving plate with small amplitude in an inviscid fluid, hopefully being a starting point for approaching the interaction of two flapping wings. The useful tools, Plemelj's formulas and the Hilbert problem, are introduced.
590 $a School code: 0262.
650 4 $a Mathematics. $3 515831
650 4 $a Mechanics. $3 525881
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710 2 $a The University of Wisconsin - Madison. $b Mathematics. $3 2101076
773 0 $t Dissertation Abstracts International $g 76-11B(E).
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791 $a Ph.D.
792 $a 2015
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3712607