Numerical solution of free and moving boundary problems on fixed and arbitrary deforming meshes

Free Surface and Moving Boundary Problems (FSMBP) involve the tracking of a surface or boundary on which a balance condition (e.g., mass and heat) has to be met. FSMBP commonly occur in engineering disciplines and the development of numerical tools for handling them are of importance in industry. In this thesis a range of robust and efficient numerical algorithms for the analysis of free surface and moving boundary problems are developed.; The two main numerical approaches for tracking a free surface or moving boundary are (i) the solution of an auxiliary phase fraction variable on a fixed grid or (ii) a deforming front tracking grid. In the first part of this work, an arbitrary Lagrangian Eulerian enthalpy scheme for dealing with diffusion controlled solidification problems, i.e. Stefan Problems, is developed. This scheme can be used to generate both fixed and deforming grid methods for tracking the phase front. The efficiency of the arbitrary Lagrangian Eulerian enthalpy scheme is demonstrated on solving a range of solidification problems taken from recent literature. Following this, fixed and deforming grid methods are developed for the tracking of the filling surface during a polymer molding process. These method are validated on a range of one, two and three dimensional filling problems; comparing predictions with experiments, analytical solutions and recent literature. Many free surface and moving boundary problems involve fluid flow and this thesis concludes with the presentation and application of a finite element control volume fluid flow solver which is suitable for the analysis of free surface and moving boundary problems. Throughout this study the underlying theme is the development of both fixed and deforming grid solutions for solving important free and moving boundary problems.