Modelling the phase change (e.g. solidification, dissolution, melting) of a solid is challenging because of the need to track the fluid-solid interface. In this chapter, we review the most common computational approaches for solving fluid flow and phase change problems. We focus on single-domain techniques adapted from porous media theory to simulate such processes. Unlike others, the single-domain approach does not necessitate complex remeshing strategies and can handle transition zones between the fluid and the solid. We discuss the enthalpy-porosity approach to simulate melting and solidification and the micro-continuum approach to simulate precipitation and dissolution of solid minerals. Finally, we use the model to investigate the solidification-melting of gallium as well as dissolution instabilities.