Sharp interface approaches and deep learning techniques for multiphase flows

We present a review on numerical methods for simulating multiphase and free surface flows. We focus in particular on numerical methods that seek to preserve the discontinuous nature of the solutions across the interface between phases. We provide a discussion on the Ghost-Fluid and Voronoi Interface methods, on the treatment of surface tension forces that avoid stringent time step restrictions, on adaptive grid refinement techniques for improved efficiency and on parallel computing approaches. We present the results of some simulations obtained with these treatments in two and three spatial dimensions. We also provide a discussion of Machine Learning and Deep Learning techniques in the context of multiphase flows and propose several future potential research thrusts for using deep learning to enhance the study and simulation of multiphase flows.