Date of Award


Degree Type


Degree Name

Doctor of Philosophy


This thesis examines various techniques for the solution of unsteady porous flow problems with moving boundaries.;A numerical method, based on the Kantorovich solution of the potential problem, and on implicit finite difference integration of the moving boundary equation, is developed. Results of the Kantorovich method are compared with the Rayleigh-Ritz solutions. Both of these direct methods yield the normal derivative on the boundary by analytic differentiation. The usual Kantorovich method is modified so that convergence is obtained regardless of grid size. Various unsteady porous flow problems with a free surface are solved by these methods, and results are compared. The Kantorovich method was slightly more efficient than the Rayleigh-Ritz method.;A multi-grid iterative scheme is applied to the Kantorovich method to accelerate the rate of convergence. A comparison of the multi-grid results and line SOR results are presented. The multi-grid procedure was clearly more efficient than the line SOR procedure.;A co-ordinate transformation technique based on the transformation of the variational integral, rather than the differential equations, is used to solve various unsteady flow problems. This method requires only the first derivative of the moving boundary and no flow boundary conditions are simply the natural boundary conditions of the variational problem. Although the co-ordinate transformation method was less efficient than the Kantorovich method it is a much more versatile numerical procedure.;A co-ordinate transformation technique is applied to the problem of unsteady movement of an interface between two fluids of different densities in a porous medium. Results are determined for three distinct problems. A qualitative analysis supports the validity of the solutions for all three problems.



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