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In two-phase flow, accurately capturing sharp interfaces is essential. Physics-Informed Neural Networks (PINNs) provide a new way to capture interfaces. This paper introduces a new framework that uses Discrete-time Physics-Informed Neural Networks (...

In this article, the flow instabilities during the rise of a single bubble in a narrow vertical tube are studied using a transient two-dimensional/axisymmetric model. To predict the shape of the bubble deformation, the Navier-Stokes equations in ...

A new approach based on volume preserving motion by mean curvature for treating surface tension in two-phase flows is introduced. Many numerical tests and a theoretical justification are included which provide evidence regarding the efficacy of the new ...

A new class of algorithms that preserve mass exactly for incompressible flows on a Cartesian mesh are presented. They amount to piecewise-linear, area-preserving mappings of tessellations of the plane. They are equivalent to Volume-of-Fluid (VOF) ...

Volume-of-fluid (VOF) methods are popular for the direct numerical simulation of time-dependent viscous incompressible flow of multiple liquids. As in any numerical method, however, it has its weaknesses, namely, for flows in which the capillary force ...