Numerical grid generation and its application in the solution of a model of the vacuum-arc remelting (VAR) process
Numerical grid generation and its application in the solution of a model of the vacuum-arc remelting (VAR) process
In the first part of this thesis, we investigate the generation of body-fitted grids using finite difference techniques in arbitrary regions. Specimen partial differential equations (p.d.e.) in arbitrary domains are solved numerically using finite difference methods and body-fitted grids and the accuracy of numerical solutions to these specimen p.d.e.s. is tested. Simple modifications to the basic grid generation method are implemented in an attempt to improve the accuracy of the numerical solutions.
Forcing terms are added to the partial differential grid generation equations and their behaviour is analysed in the analagous one-dimensional case. The results from the one-dimensional analysis give us a better understanding of the forced two-dimensional grid generation equations which therefore allows us to provide better starting values for the generation process. The accuracy of numerical solutions to further specimen p.d.e.s. with known boundary layer-type behaviour is then examined. Variations of the forced grid generation equations are considered and tested.
Methods of solution-adaptive grid generation are examined in an attempt to automatically produce grids which are tailored to a specific problem which is to be solved numerically with the body-fitted grid. The effect of the modification of the parameters in the solution-adaptive grid generation method is explored and then the accuracy of sample p.d.e.s. solved numerically using this grid generation method is examined.
In the second part of this thesis, we derive the equations which model the Vacuum-Arc Remelting (VAR) process. These equations are solved with body-fitted grid generation techniques and the results are compared with the results of previous authors. A different form for the input source for the VAR process is tested and the results obtained with a body-fitted grid are presented. The method of solution-adaptive grid generation already examined in this thesis is used in the solution of the VAR modelling equations and the results are compared with those results obtained with a regular grid. Tests are conducted with varying values of the parameters in the modelling equations to determine which parameters most affect the behaviour of the solution of the VAR equations. Conclusions are drawn regarding the behaviour of the solution of the VAR equations.
University of Southampton
1998
Polton, Richard
(1998)
Numerical grid generation and its application in the solution of a model of the vacuum-arc remelting (VAR) process.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
In the first part of this thesis, we investigate the generation of body-fitted grids using finite difference techniques in arbitrary regions. Specimen partial differential equations (p.d.e.) in arbitrary domains are solved numerically using finite difference methods and body-fitted grids and the accuracy of numerical solutions to these specimen p.d.e.s. is tested. Simple modifications to the basic grid generation method are implemented in an attempt to improve the accuracy of the numerical solutions.
Forcing terms are added to the partial differential grid generation equations and their behaviour is analysed in the analagous one-dimensional case. The results from the one-dimensional analysis give us a better understanding of the forced two-dimensional grid generation equations which therefore allows us to provide better starting values for the generation process. The accuracy of numerical solutions to further specimen p.d.e.s. with known boundary layer-type behaviour is then examined. Variations of the forced grid generation equations are considered and tested.
Methods of solution-adaptive grid generation are examined in an attempt to automatically produce grids which are tailored to a specific problem which is to be solved numerically with the body-fitted grid. The effect of the modification of the parameters in the solution-adaptive grid generation method is explored and then the accuracy of sample p.d.e.s. solved numerically using this grid generation method is examined.
In the second part of this thesis, we derive the equations which model the Vacuum-Arc Remelting (VAR) process. These equations are solved with body-fitted grid generation techniques and the results are compared with the results of previous authors. A different form for the input source for the VAR process is tested and the results obtained with a body-fitted grid are presented. The method of solution-adaptive grid generation already examined in this thesis is used in the solution of the VAR modelling equations and the results are compared with those results obtained with a regular grid. Tests are conducted with varying values of the parameters in the modelling equations to determine which parameters most affect the behaviour of the solution of the VAR equations. Conclusions are drawn regarding the behaviour of the solution of the VAR equations.
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Published date: 1998
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Local EPrints ID: 464108
URI: http://eprints.soton.ac.uk/id/eprint/464108
PURE UUID: a79cdeaf-717e-4f52-9f5a-36cc975caad9
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Date deposited: 04 Jul 2022 21:18
Last modified: 04 Jul 2022 21:18
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Author:
Richard Polton
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