Computational interface capturing methods for phase change in porous media

Abstract

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 steam-water 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 results for the two-dimensional problem are also presented.