A conservative cut-cell/front-tracking method for interface-resolved two-phase flow simulations

Front-tracking methods simulate two-phase flows by using Lagrangian markers to explicitly track the interface between the phases, as well as a fixed Eulerian grid to resolve the flow field. Usually, the approach is combined with a one-field model of the flow field. This model uses a unique set of equations, blending the properties of the two phases in the interfacial region. This article proposes a numerical method that combines a front-tracking representation of the interface and a cut-cell discretisation of the flow field. By cutting the Eulerian grid to conform to the interface, the cut-cell discretisation can resolve the two phases separately with a two-field formalism. The present method uses a three-dimensional Cartesian staggered grid system and finite-volume schemes, which enforce strict local conservation of momentum, whereas a projection method imposes the divergence-free condition at the level of Cartesian cells. It is combined with a volume-preserving displacement of the Lagrangian mesh to ensure mass conservation. The numerical method is evaluated for a stationary spherical droplet, an oscillating droplet, a periodic array of bubbles, and a rising oblate bubble in planar zigzagging. The numerical method is stable and provides more accurate results than a baseline one-field/front-tracking method with similar spatial schemes, as the numerical method can explicitly impose accurate values of interfacial momentum transfers.