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A Variational Implementation of Imme...

Mishra, Abhishek.

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A Variational Implementation of Immersed Boundary Method for Fluid-Structure Interaction Problems.

Record Type:	Electronic resources : Monograph/item
Title/Author:	A Variational Implementation of Immersed Boundary Method for Fluid-Structure Interaction Problems./
Author:	Mishra, Abhishek.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	71 p.
Notes:	Source: Masters Abstracts International, Volume: 81-04.
Contained By:	Masters Abstracts International81-04.
Subject:	Aerospace engineering. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13885516
ISBN:	9781085773782

A Variational Implementation of Immersed Boundary Method for Fluid-Structure Interaction Problems.
Mishra, Abhishek.

A Variational Implementation of Immersed Boundary Method for Fluid-Structure Interaction Problems. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 71 p.

Source: Masters Abstracts International, Volume: 81-04.

Thesis (M.S.)--State University of New York at Buffalo, 2019.

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

The Immersed Boundary Method (IBM) was designed by Peskin for modeling fluid-structure interaction (FSI) problems, where a structure is completely immersed in a fluid, in contrast to the arbitrary Lagrangian-Eulerian (ALE) method, which consists of a conforming interface between the fluid and the solid. In the original IBM, the Navier-Stokes equations are considered everywhere and the presence of the immersed solid is taken into account using a Dirac delta distribution term which depends on the position of the solid. Recently, a finite element version of the IBM was developed by Boffi et. al., which avoids explicit treatment of the Dirac delta distribution term. In this approach, equations governing the fluid and solid motion are discretized using finite element method (FEM). The Navier-Stokes equations are solved first using the solid position at previous time step, and then the solid position is updated according to the computed velocity. A modification to this approach was also proposed by Boffi et. al., a fictitious domain formulation of the finite element IBM, that makes use of a distributed Lagrange multiplier, enforcing a constraint on the velocity matching of the solid and the fluid.In this work, we propose a new formulation based on the nonlinear solid mechanics formulations, which properly enforces incompressibility constraints, that corrects any volumetric instabilities that may occur due to discretization of incompressible hyperelastic materials. We numerically investigate some FSI problems using our proposed formulation. The computational algorithm for the implementation of our IBM formulation has been developed using GRINS, a C++ software framework, based on the libMesh finite element library, designed to simulate multiphysics systems of partial differential equations (PDEs) using FEM.

ISBN: 9781085773782Subjects--Topical Terms:

1002622
Aerospace engineering.
Subjects--Index Terms:

Distributed Lagrange multiplier

A Variational Implementation of Immersed Boundary Method for Fluid-Structure Interaction Problems.
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100 1 $a Mishra, Abhishek. $3 3512988
245 1 0 $a A Variational Implementation of Immersed Boundary Method for Fluid-Structure Interaction Problems.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 71 p.
500 $a Source: Masters Abstracts International, Volume: 81-04.
500 $a Advisor: Bauman, Paul T.
502 $a Thesis (M.S.)--State University of New York at Buffalo, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a The Immersed Boundary Method (IBM) was designed by Peskin for modeling fluid-structure interaction (FSI) problems, where a structure is completely immersed in a fluid, in contrast to the arbitrary Lagrangian-Eulerian (ALE) method, which consists of a conforming interface between the fluid and the solid. In the original IBM, the Navier-Stokes equations are considered everywhere and the presence of the immersed solid is taken into account using a Dirac delta distribution term which depends on the position of the solid. Recently, a finite element version of the IBM was developed by Boffi et. al., which avoids explicit treatment of the Dirac delta distribution term. In this approach, equations governing the fluid and solid motion are discretized using finite element method (FEM). The Navier-Stokes equations are solved first using the solid position at previous time step, and then the solid position is updated according to the computed velocity. A modification to this approach was also proposed by Boffi et. al., a fictitious domain formulation of the finite element IBM, that makes use of a distributed Lagrange multiplier, enforcing a constraint on the velocity matching of the solid and the fluid.In this work, we propose a new formulation based on the nonlinear solid mechanics formulations, which properly enforces incompressibility constraints, that corrects any volumetric instabilities that may occur due to discretization of incompressible hyperelastic materials. We numerically investigate some FSI problems using our proposed formulation. The computational algorithm for the implementation of our IBM formulation has been developed using GRINS, a C++ software framework, based on the libMesh finite element library, designed to simulate multiphysics systems of partial differential equations (PDEs) using FEM.
590 $a School code: 0656.
650 4 $a Aerospace engineering. $3 1002622
650 4 $a Applied mathematics. $3 2122814
650 4 $a Computational physics. $3 3343998
653 $a Distributed Lagrange multiplier
653 $a Fictitious domain
653 $a Finite element method
653 $a Immersed boundary method
653 $a Variational
653 $a Volumetric stabilization
690 $a 0538
690 $a 0364
690 $a 0216
710 2 $a State University of New York at Buffalo. $b Mechanical and Aerospace Engineering. $3 1017747
773 0 $t Masters Abstracts International $g 81-04.
790 $a 0656
791 $a M.S.
792 $a 2019
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13885516