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A locally conservative Galerkin (LCG) finite element method for convection-diffusion and Navier-Stokes equations. / Craig George Thomas

Swansea University Author: Craig George Thomas

Abstract

In this thesis, an element-wise locally conservative Galerkin (LCG) finite element method is presented. The LCG method has been shown here to be successful in solving equations of scalar-transport, and the incompressible Navier-Stokes equations. The LCG approach facilitates an element-by-element sol...

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Published: 2006
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42342
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last_indexed 2018-08-03T10:09:54Z
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spelling 2018-08-02T16:24:28.9010008 v2 42342 2018-08-02 A locally conservative Galerkin (LCG) finite element method for convection-diffusion and Navier-Stokes equations. bf5e6da11ed9e317e549e6e8e947b761 NULL Craig George Thomas Craig George Thomas true true 2018-08-02 In this thesis, an element-wise locally conservative Galerkin (LCG) finite element method is presented. The LCG method has been shown here to be successful in solving equations of scalar-transport, and the incompressible Navier-Stokes equations. The LCG approach facilitates an element-by-element solution and obtains a continuous and unique nodal solution from the surrounding element contributions, via averaging. A simple numerical flux establishes continuity at the edges between neighbouring elements. This allows the system of discrete equations to be solved over each elemental sub-domain, greatly simplifying the solution procedure. The method explicitly establishes local elementwise conservation, and after the averaging procedure a residual flux appears on the global boundary. It is this flux which gives the LCG method global conservation, regardless of prescribed boundary conditions. Aspects research are: the mathematical formulation; explicit and implicit discretisations; edge flux calculation procedures; development and implementation of Petrov-Galerkin and characteristic based methods; and finally matrix-free LCG methods for steady and unsteady incompressible flows. Evaluation of all the proposed LCG methods has been given, showing the methods to be accurate and robust. E-Thesis Computer science.;Applied mathematics. 31 12 2006 2006-12-31 COLLEGE NANME Engineering COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:28.9010008 2018-08-02T16:24:28.9010008 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Craig George Thomas NULL 1 0042342-02082018162446.pdf 10798050.pdf 2018-08-02T16:24:46.9370000 Output 12403449 application/pdf E-Thesis true 2018-08-02T16:24:46.9370000 false
title A locally conservative Galerkin (LCG) finite element method for convection-diffusion and Navier-Stokes equations.
spellingShingle A locally conservative Galerkin (LCG) finite element method for convection-diffusion and Navier-Stokes equations.
Craig George Thomas
title_short A locally conservative Galerkin (LCG) finite element method for convection-diffusion and Navier-Stokes equations.
title_full A locally conservative Galerkin (LCG) finite element method for convection-diffusion and Navier-Stokes equations.
title_fullStr A locally conservative Galerkin (LCG) finite element method for convection-diffusion and Navier-Stokes equations.
title_full_unstemmed A locally conservative Galerkin (LCG) finite element method for convection-diffusion and Navier-Stokes equations.
title_sort A locally conservative Galerkin (LCG) finite element method for convection-diffusion and Navier-Stokes equations.
author_id_str_mv bf5e6da11ed9e317e549e6e8e947b761
author_id_fullname_str_mv bf5e6da11ed9e317e549e6e8e947b761_***_Craig George Thomas
author Craig George Thomas
author2 Craig George Thomas
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 element-wise locally conservative Galerkin (LCG) finite element method is presented. The LCG method has been shown here to be successful in solving equations of scalar-transport, and the incompressible Navier-Stokes equations. The LCG approach facilitates an element-by-element solution and obtains a continuous and unique nodal solution from the surrounding element contributions, via averaging. A simple numerical flux establishes continuity at the edges between neighbouring elements. This allows the system of discrete equations to be solved over each elemental sub-domain, greatly simplifying the solution procedure. The method explicitly establishes local elementwise conservation, and after the averaging procedure a residual flux appears on the global boundary. It is this flux which gives the LCG method global conservation, regardless of prescribed boundary conditions. Aspects research are: the mathematical formulation; explicit and implicit discretisations; edge flux calculation procedures; development and implementation of Petrov-Galerkin and characteristic based methods; and finally matrix-free LCG methods for steady and unsteady incompressible flows. Evaluation of all the proposed LCG methods has been given, showing the methods to be accurate and robust.
published_date 2006-12-31T03:52:46Z
_version_ 1763752612420648960
score 11.013082

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