A review on computational modelling of phase-transition problems

Phase-transition problems are ubiquitous in science and engineering. They have been widely studied via theory, experiments and computations. This paper reviews the main challenges associated with computational modelling of phase-transition problems, addressing both model development and numerical discretization of the resulting equations. We focus on classical phase-transition problems, including liquid-solid, gas-liquid and solid-solid transformations. Our review has a strong emphasis on the treatment of interfacial phenomena and the phase-field method. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.