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We present a novel mathematical model of two-phase interfacial flows. It is based on the Entropically Damped Artificial Compressibility (EDAC) model, coupled with a diffuse-interface (DI) variant of the so-called one-fluid formulation for interface capturing. The proposed EDAC-DI model conserves mass and momentum. We find appropriate values of the model parameters, in particular the numerical interface width, the interface mobility and the speed of sound. The EDAC-DI governing equations are of the mixed parabolic–hyperbolic type. For such models, the local spatial schemes along with an explicit time integration provide a convenient numerical handling together with straightforward and efficient parallelisation of the solution algorithm. The weakly-compressible approach to flow modelling, although computationally advantageous, introduces some difficulties that are not present in the truly incompressible approaches to interfacial flows. These issues are covered in detail. We propose a robust numerical solution methodology which significantly limits spurious deformations of the interface and provides oscillation-free behaviour of the flow fields. The EDAC-DI solver is verified quantitatively in the case of a single, steady water droplet immersed in gas. The pressure jump across the interface is in good agreement with the theoretical prediction. Then, a study of binary droplets coalescence and break-up in two chosen collision regimes is performed. The topological changes are solved correctly without numerical side effects. The computational cost incurred by the stiffness of the governing equations (due to the finite speed of sound and the interface diffusion term) can be overcome by a massively parallel execution of the solver. We achieved an attractively short computation time when our EDAC-DI code is executed on a single, desktop-type Graphics Processing Unit.

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