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Title: A locally conservative Galerkin (LCG) finite element method for convection-diffusion and Navier-Stokes equations
Author: Thomas, Craig George
Awarding Body: University of Wales, Swansea
Current Institution: Swansea University
Date of Award: 2006
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available