document: Multi-phase flows are common, in fact quite general, in environmental and industrial processes. Broadly these may be modelled as continuous problems where phases are mixed (e.g. oil–water homogenisation [36], sediment transport [18]) or interface problems where phases are distinct and interact at the interface (e.g. gas-assisted injection moulding [21], liquid jet breakup [40]). In some cases flows start as interface problems but as mixing occurs at the interface they become effectively continuous, at least locally. Air entrainment, perhaps due to wave breaking, is an obvious example. We consider here two-phase interface problems where the interface remains distinct and the density difference is high, e.g. air and water, and where one phase may be considered incompressible. The interface is transient and may become highly distorted and interconnected. Such problems have been tackled with mesh-based methods using periodic (or adaptive) re-meshing or additional phase tracking functions [40]. However, these approaches can be time-consuming to implement and prone to errors in surface representation [50] or mass conservation [34].
extractive_keyphrases: air distorted and interconnected environmental and industrial processes interface problems liquid jet breakup mixing oil–water homogenisation phases are mixed phase tracking functions sediment transport water wave breaking
abstractive_keyphrases: air entrainment gas-assisted injection moulding mesh-based methods multi-phase flows re-meshing two-phase interface problems