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Numerical Approaches for Solving Free Surface Flows pp. 351-384 $100.00
Authors:  (Laura B. Battaglia, Jorge D’Elia, Mario A. Storti, Centro Internacional de Metodos Computacionales en Ingenieria, Instituto de Desarrollo Tecnologico para la Industria Quimica (INTEC) Universidad Nacional del Litoral, Santa Fe, Argentina, and others)
A free surface is defined as an interface between two fluids, where the lighter phase, which is usually a gas, has negligible effect over the other due to its very low values of density and viscosity. Free surface flows are common issues among several engineering disciplines, such as civil, mechanical or naval. Some typical problems are open channel flows, sloshing in tanks for storing or transporting liquids, and mold filling, among others. Different numerical methods have been developed for solving these kind of flows, being the most popular classification of techniques the one that refers to “interface tracking” and “interface capturing” methods. On one side, the interface tracking ap- proaches are based on considering the free surface as a boundary of the domain, and defining over that boundaries some entities such as nodes or element edges of a finite element method mesh, in such a way that the fluid flow problem is solved over a sin- gle liquid phase. On the other side, interface capturing approximations are based on marking functions that indicate which part of the domain is occupied by the liquid, and which other is occupied by the gaseous phase, such that the interface position is “cap- tured” over certain values of the marking function. In the present chapter, two finite element methods for solving free surface flows are described: an interface tracking technique developed over an arbitrary Lagrangian-Eulerian framework, and a level set interface capturing proposal. Each approach has been considered for solving different free surface flow problems, regarding the capabilities of the methods. 

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Numerical Approaches for Solving Free Surface Flows pp. 351-384