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Sharp interface approaches and deep learning techniques for multiphase flows. (English) Zbl 1451.76131

Summary: 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.

MSC:

76T10 Liquid-gas two-phase flows, bubbly flows
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N08 Finite volume methods for boundary value problems involving PDEs
76D45 Capillarity (surface tension) for incompressible viscous fluids
68T07 Artificial neural networks and deep learning
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