Date of Award


Degree Type


Degree Name

Doctor of Philosophy


This thesis obtains numerical solutions for three instability problems.;The first is a Rayleigh-Taylor interfacial instability problem. Numerical solutions are obtained using a co-ordinate transformation technique and two approaches are tested for use in solving the field equation: (a) transformation and extremization of the variational integral, and (b) transformation of the differential equation itself. The latter is also tested with the use of higher order finite difference formulae. Solutions are generated with the most suitable method and compared with the predictions of Nayfeh's non-linear perturbation theory. While there is good qualitative agreement it is found that the quantitative agreement degrades with increases in the magnitude of the interfacial distortion.;The second problem is a generalized Stefan problem that models the behaviour of the interface between two components of a system that is undergoing melting or solidification. A co-ordinate transformation is employed and the numerical results are compared with the qualitative predictions of the linear perturbation theory of Chadam and Ortoleva. Agreement is excellent.;The third problem examines the onset of convective instability in a porous medium that is saturated with a fluid that has a temperature-depenent viscosity similar to that of heavy oil. A linear stability analysis is performed to determine the onset conditions and numerical solutions are generated for convective flow near these conditions. It is found that problems with convergence arise when the numerical method is used with small grid sizes.



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