The Numerical Solution of One-Dimensional Phase Change Problems Using an Adaptive Moving Mesh Method

An adaptive moving mesh method is developed for the numerical solution of an enthalpy formulation of heat conduction problems with a phase change. The algorithm is based on a very simple mesh modification strategy that allows the smooth evolution of mesh nodes to track interfaces. At each time step the nonlinear enthalpy equation is solved using a novel semi-implicit moving mesh discretisation which is shown to possess a unique solution. Numerical examples are given for a two-phase freezing problem, a model of a spot-welding process, and a three-phase problem with a varying number of interfaces. These test cases demonstrate the accuracy and effectiveness of the overall strategy.