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Computational methods for incompressible fluid flows with reference to interface modelling by an extended finite element method. / James MacFadden

Swansea University Author: James MacFadden

Abstract

In this thesis an implicit Semi-Discrete Stabilized eXtended Finite Element formulation has been successfully developed and implemented for laminar Newtonian incompressible fluid flows. In doing so we have contributed to the research into the field of incompressible fluid flows, multiphase flow and...

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Published: 2006
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42810
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first_indexed 2018-08-02T18:55:36Z
last_indexed 2018-08-03T10:11:09Z
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spelling 2018-08-02T16:24:30.5389960 v2 42810 2018-08-02 Computational methods for incompressible fluid flows with reference to interface modelling by an extended finite element method. 4ffe7a25adbff6af1b250cf7cfda1995 NULL James MacFadden James MacFadden true true 2018-08-02 In this thesis an implicit Semi-Discrete Stabilized eXtended Finite Element formulation has been successfully developed and implemented for laminar Newtonian incompressible fluid flows. In doing so we have contributed to the research into the field of incompressible fluid flows, multiphase flow and fluid-rigid body interaction. The fluid flows are governed by the incompressible viscous Navier-Stokes equations, using a Finite Element formulation to model the fluid behaviour numerically. A Semi-Discrete time integration scheme was implemented, discretizing in space, leaving the system of ordinary differential equations to be integrated in time. Initially the classical Galerkin method is used to formulate the boundary value problem from the governing equations, however stability issues due to incompressibility and dominant advection terms force the implementation of the stabilized formulation, i.e. SUPG/PSPG. This approach gives greater flexibility in choice of velocity/pressure interpolations, such as equal order functions. The time integration schemes (Generalized alpha method and Generalized Midpoint rule) were compared and contrasted, with the Generalized alpha method demonstrating improved convergence. The highly nonlinear form of the governing equations required an implicit iterative solver and the Newton-Raphson procedure was chosen. Several tests were performed throughout the formulation of the boundary value problem to validate the implementation. The result, a robust, efficient and accurate unsteady incompressible Newtonian fluid formulation. extended FEM was introduced by adding terms to the FEM formulation in a Partition of Unity framework. With the addition of complex solution procedures X-FEM was implemented and tested for multiphase and fluid-rigid body interaction, demonstrating the attractive qualities of this method. E-Thesis Computer engineering.;Fluid mechanics. 31 12 2006 2006-12-31 COLLEGE NANME Engineering COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:30.5389960 2018-08-02T16:24:30.5389960 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised James MacFadden NULL 1 0042810-02082018162523.pdf 10807586.pdf 2018-08-02T16:25:23.6900000 Output 23525494 application/pdf E-Thesis true 2018-08-02T16:25:23.6900000 false
title Computational methods for incompressible fluid flows with reference to interface modelling by an extended finite element method.
spellingShingle Computational methods for incompressible fluid flows with reference to interface modelling by an extended finite element method.
James MacFadden
title_short Computational methods for incompressible fluid flows with reference to interface modelling by an extended finite element method.
title_full Computational methods for incompressible fluid flows with reference to interface modelling by an extended finite element method.
title_fullStr Computational methods for incompressible fluid flows with reference to interface modelling by an extended finite element method.
title_full_unstemmed Computational methods for incompressible fluid flows with reference to interface modelling by an extended finite element method.
title_sort Computational methods for incompressible fluid flows with reference to interface modelling by an extended finite element method.
author_id_str_mv 4ffe7a25adbff6af1b250cf7cfda1995
author_id_fullname_str_mv 4ffe7a25adbff6af1b250cf7cfda1995_***_James MacFadden
author James MacFadden
author2 James MacFadden
format E-Thesis
publishDate 2006
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
active_str 0
description In this thesis an implicit Semi-Discrete Stabilized eXtended Finite Element formulation has been successfully developed and implemented for laminar Newtonian incompressible fluid flows. In doing so we have contributed to the research into the field of incompressible fluid flows, multiphase flow and fluid-rigid body interaction. The fluid flows are governed by the incompressible viscous Navier-Stokes equations, using a Finite Element formulation to model the fluid behaviour numerically. A Semi-Discrete time integration scheme was implemented, discretizing in space, leaving the system of ordinary differential equations to be integrated in time. Initially the classical Galerkin method is used to formulate the boundary value problem from the governing equations, however stability issues due to incompressibility and dominant advection terms force the implementation of the stabilized formulation, i.e. SUPG/PSPG. This approach gives greater flexibility in choice of velocity/pressure interpolations, such as equal order functions. The time integration schemes (Generalized alpha method and Generalized Midpoint rule) were compared and contrasted, with the Generalized alpha method demonstrating improved convergence. The highly nonlinear form of the governing equations required an implicit iterative solver and the Newton-Raphson procedure was chosen. Several tests were performed throughout the formulation of the boundary value problem to validate the implementation. The result, a robust, efficient and accurate unsteady incompressible Newtonian fluid formulation. extended FEM was introduced by adding terms to the FEM formulation in a Partition of Unity framework. With the addition of complex solution procedures X-FEM was implemented and tested for multiphase and fluid-rigid body interaction, demonstrating the attractive qualities of this method.
published_date 2006-12-31T03:53:41Z
_version_ 1763752670078697472
score 11.014067

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