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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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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 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.
Keywords: Computer science.;Applied mathematics.
College: College of Engineering