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Efficient and Accurate Numerical Met...

Bao, Yuan Xun.

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Efficient and Accurate Numerical Methods for Fluid-Structure and Fluid-Particle Interactions.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Efficient and Accurate Numerical Methods for Fluid-Structure and Fluid-Particle Interactions./
Author:	Bao, Yuan Xun.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
Description:	171 p.
Notes:	Source: Dissertation Abstracts International, Volume: 80-03(E), Section: B.
Contained By:	Dissertation Abstracts International80-03B(E).
Subject:	Applied mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10751152
ISBN:	9780438633933

Efficient and Accurate Numerical Methods for Fluid-Structure and Fluid-Particle Interactions.
Bao, Yuan Xun.

Efficient and Accurate Numerical Methods for Fluid-Structure and Fluid-Particle Interactions. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 171 p.

Source: Dissertation Abstracts International, Volume: 80-03(E), Section: B.

Thesis (Ph.D.)--New York University, 2018.

We present two efficient and accurate numerical methods for simulating elastic and rigid structures immersed in fluids. In the first part, we focus on the Immersed Boundary (IB) method for studying fluid-structure interaction in problems involving an elastic structure immersed in a viscous incompressible fluid at finite Reynolds numbers. It is well-known that the conventional IB method suffers from poor volume conservation. This arises because the interpolated Lagrangian velocity is not generally divergence-free. We develop a Divergence-Free Immersed Boundary (DFIB) method that substantially reduces the volume loss in an immersed body as it moves and deforms in the process of interacting with the fluid. We introduce a new velocity-interpolation scheme with the property that the interpolated velocity field in which the structure moves is continuously differentiable, and satisfies a continuous divergence-free condition. We also develop a new force-spreading scheme that is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that DFIB is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Furthermore, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods.

ISBN: 9780438633933Subjects--Topical Terms:

2122814
Applied mathematics.

Efficient and Accurate Numerical Methods for Fluid-Structure and Fluid-Particle Interactions.
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100 1 $a Bao, Yuan Xun. $3 3432037
245 1 0 $a Efficient and Accurate Numerical Methods for Fluid-Structure and Fluid-Particle Interactions.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2018
300 $a 171 p.
500 $a Source: Dissertation Abstracts International, Volume: 80-03(E), Section: B.
500 $a Advisers: Aleksandar Donev; Leslie F. Greengard.
502 $a Thesis (Ph.D.)--New York University, 2018.
520 $a We present two efficient and accurate numerical methods for simulating elastic and rigid structures immersed in fluids. In the first part, we focus on the Immersed Boundary (IB) method for studying fluid-structure interaction in problems involving an elastic structure immersed in a viscous incompressible fluid at finite Reynolds numbers. It is well-known that the conventional IB method suffers from poor volume conservation. This arises because the interpolated Lagrangian velocity is not generally divergence-free. We develop a Divergence-Free Immersed Boundary (DFIB) method that substantially reduces the volume loss in an immersed body as it moves and deforms in the process of interacting with the fluid. We introduce a new velocity-interpolation scheme with the property that the interpolated velocity field in which the structure moves is continuously differentiable, and satisfies a continuous divergence-free condition. We also develop a new force-spreading scheme that is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that DFIB is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Furthermore, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods.
520 $a In the second part, we present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics of two-dimensional periodic suspensions of rigid particles immersed in a Stokes fluid. At small scales and low Reynolds numbers, the motion of immersed particles is strongly influenced by thermal fluctuations, giving rise to Brownian motion strongly correlated with hydrodynamic effects. We develop a novel approach for generating Brownian displacements that arise in response to the thermal fluctuations in the fluid. Our approach relies on a first-kind boundary integral formulation of a mobility problem in which a random surface velocity is prescribed on the particle surface, with zero mean and covariance proportional to the Green's function for Stokes flow (Stokeslet). This approach yields an algorithm that scales linearly in the number of particles for both deterministic and stochastic dynamics, handles particles of complex shape, achieves high order of accuracy, and can be generalized to three dimensions and other boundary conditions. We show that Brownian displacements generated by our method obey the discrete fluctuation-dissipation balance relation (DFDB). FBIM provides the key ingredient for time integration of the overdamped Langevin equations for Brownian suspensions of rigid particles. We demonstrate that FBIM obeys DFDB by performing equilibrium BD simulations of suspensions of starfish-shaped bodies using a random finite difference temporal integrator.
590 $a School code: 0146.
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650 4 $a Fluid mechanics. $3 528155
650 4 $a Computational physics. $3 3343998
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710 2 $a New York University. $b Mathematics. $3 1019424
773 0 $t Dissertation Abstracts International $g 80-03B(E).
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