The subject of this book is the development of an efficient numerical method capable of predicting the flow behavior of two-phase immiscible fluids. In the quest of an accurate and robust numerical method for the modeling of two-phase flows, one has to keep in mind the intrinsic properties and difficulties associated with the problem: (i) those flows are mostly three-dimensional, (ii) the interface might encounter a lot of topology changes, (iii) large jumps of density and viscosity might exist across the interface, (iv) surface tension forces may play a very important role in the interface dynamics. Hence, the influence of this force should be accurately evaluated and incorporated into the model, (v) mass conservation is of primary importance. All these issues are addressed, and special techniques are proposed for their treatment. The chosen method combines a pressure stabilized finite element method for the Navier Stokes equations with a discontinuous Galerkin method for the level set equation. Such a combination of those numerical methods results in a simple and effective algorithm that allows to simulate diverse flow regimes presenting large density and viscosity ratios.

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