| Summary: | In this thesis, computational interface capturing methods for mathematical
models related to fluid phase change processes in porous media are studied.
The mathematical models are often singular and degenerate, which
contributes to the computational difficulty.
An analysis of a smoothing method applied to a one dimensional free
interface problem is presented. An asymptotic analysis shows the dependence
of the error in the computed interface location on the chosen small smoothing
radius.
Numerical convergence studies are performed for existing capturing methods
applied to simple, scalar, moving interface problems, for later comparison
with convergence rates for a new capturing method applied to a coupled, vector
model problem.
A model problem for two-phase fluid flow and heat transfer with phase
change in a porous medium is described. The model is based on a steamwater
mixture in sand. Under certain conditions, a two-phase zone, in which
liquid and vapour coexist, is separated from a region of only vapour by an
interface. Two numerical methods are described for locating the interface
in the one-dimensional, steady-state problem; one of these is based on an
existing method, while the other uses the method of Residual Velocities.
Agreement between solutions from these two methods is demonstrated, and
the results from the steady-state computations are used as benchmarks for
the numerical results for the transient problem.
It is shown that methods such as front-tracking and the level-set method
are not practical for the solution of the transient problem, due to the indeterminate
nature of the interface velocity, in common with similar degenerate
diffusion problems. An interface-capturing method, based on a two-phase
mixture formulation, is presented. A finite volume method is developed, and
numerical results show evolution to the correct steady-state. Furthermore,
similarity solutions are found, and the interface is shown to propagate at the
correct velocity, by way of a numerical convergence study. Numerical resultsfor the two-dimensional problem are also presented. === Science, Faculty of === Mathematics, Department of === Graduate
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