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Lagrangian particles and the modeling of dynamic surfaces


Researches in computational simulation of fluid flows are present both on Engineers, where its goals are technological aspects, and on computer graphics, where its goals are realistic and real-time simulations. However, two issues are faced by the state-of-art of computational simulation of fluid flows: (a) the fluid representation with arbitrary topology and geometry and (b) the definition of an algebraic system from governing equations regarding contour conditions. Eulerian formulations, specifically those ones based on level-set (LS) approaches, have been broadly used for applications related to free-surface and multiphase flows, not only on Engineering areas but also in computer graphics. Such facts arise due to some advantages: their capability to deal with topological changes naturally and their simplicity of programming. However, in LS approaches numerical issue arises which leads to gain/loss of mass, momentum and energy. This fact can produce quite poor solutions making poor the visual aspect of the simulation, which is a computer graphics requirement. Another class of methods to represent evolving interfaces is those one based on Lagrangian methods. For those, the fluid interface is given by a polygonal mesh. The main issue of these methods is the topological mesh handling during the fluid flow simulation, which is computational, expensive and is based on geometrical heuristics and user-tuned parameters. In the present project we propose the development of methods which will use only Lagrangian particles to define implicit surfaces capable of preserving physical properties of the simulated problem. We seek for developing approaches based on implicit surfaces defined by algebraic moving least squares and by matricial radial basis functions. Based on preliminary results, we believe that our approaches will be effective to preserve mass and geometry and handle topological chances of the implicit surface. (AU)

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