Moving phase boundaries have been researched for a long time by different fields of science and many interesting processes exist that involve moving interfaces, like the melting of ice, phase transformations in metals or tumor growth. To gain an overview of the field, some important formulations of moving boundary problems are described and analytic solutions presented, where possible. Three basic types of numerical approaches are emphasized and several different methods, belonging to each type, are reviewed. The model of moving interfaces is implemented in the microstructural simulation-software MatCalc. A variable-spaced-grid approach, similar to the Murray Landis method, is used to track the interface movement. In order to compute the interface velocity, the local equilibrium hypothesis is applied.
Reducing deviations from the mass balance requires inclusion of the Murray Landis correction term into the diffusion equation. Heat treatments are introduced to simulate phase transformations of iron-carbon alloys and at the end, a solidification example and a peritectic reaction, involving austenite and ferrite, are shown.