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Title: An investigation of conservative moving-mesh methods for conservation laws
Author: Arthurs, Naill
ISNI:       0000 0004 6420 9591
Awarding Body: University of Reading
Current Institution: University of Reading
Date of Award: 2016
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In this thesis we consider a class of conservation based moving mesh methods applied to hyperbolic conservation laws. We mainly concentrate on the one dimensional case with the examples of the linear advection equation, inviscid Burgers’ equation and the Buckley-Leverett equation. The moving mesh methods are generated using the conservation of mass as a method for determining the mesh velocity at the computational nodes. We use the notion of the reference space as a mathematical tool to analyse the moving mesh methods allowing us to show the accuracy, stability conditions and convergence. In addition we use the reference space as a technique for constructing new moving mesh methods which share the accuracy and stability properties of the fixed mesh scheme they are derived from. At the end of the thesis we use the knowledge gained from the scalar conservation laws to construct moving mesh methods for the isothermal equations.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available