In the present work the authors present a simplified formulation for the extension of a ghost fluid method in multidimensional space. In the proposed method, the Riemann problems at the interface are formulated along the grid rather than in a normal to the interface direction. The information that is required to construct these Riemann problems is acquired "on-the-fly" from the adjacent to the interface cells. With respect to existing multidimensional ghost fluid formulations, the method is computationally less expensive, as the procedures of determining ghost fluid regions, extending, interpolating and extrapolating variables and computing geometrical quantities are avoided. More importantly, it is markedly simple with respect to its implementation. By introducing the proposed formulation in a well-established front tracking framework we perform an extensive validation of the method and demonstrate that despite its simplicity it yields highly accurate results while remaining free of oscillations.
The aim of the present work is to study the interaction between an oscillating bubble and a free surface. We perform a series of experiments and numerical simulations and attempt to characterize both early and late stages of the interaction. The focus is on providing insight into the mechanisms of bubble-induced atomization. For this reason, we are particularly interested in characterizing the patterns and dynamics of the liquid jets that are formed at the free surface. Observations regarding the evolution of the free surface are presented by measuring the jet's surface area and volume. Finally, based on these quantities, we introduce a metric that may be used to characterize the liquid jetting and predict whether late-time atomization of the interface will occur.
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