SUMMARYA numerical method for solving three-dimensional free surface flows is presented. The technique is an extension of the GENSMAC code for calculating free surface flows in two dimensions. As in GENS-MAC, the full Navier-Stokes equations are solved by a finite difference method; the fluid surface is represented by a piecewise linear surface composed of quadrilaterals and triangles containing marker particles on their vertices; the stress conditions on the free surface are accurately imposed; the conjugate gradient method is employed for solving the discrete Poisson equation arising from a velocity update; and an automatic time step routine is used for calculating the time step at every cycle. A program implementing these features has been interfaced with a solid modelling routine defining the flow domain. A user-friendly input data file is employed to allow almost any arbitrary three-dimensional shape to be described. The visualization of the results is performed using computer graphic structures such as phong shade, flat and parallel surfaces. Results demonstrating the applicability of this new technique for solving complex free surface flows, such as cavity filling and jet buckling, are presented.

In the present work we describe a method which allows the incorporation of surface tension into the GENSMAC2D code. This is achieved on two scales. First on the scale of a cell, the surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure. The required curvature is estimated by fitting a least square circle to the free surface using the tracking particles in the cell and in its close neighbors. On a sub-cell scale, short wavelength perturbations are filtered out using a local 4-point stencil which is mass conservative. An efficient implementation is obtained through a dual representation of the cell data, using both a matrix representation, for ease at identifying neighbouring cells, and also a tree data structure, which permits the representation of specific groups of cells with additional information pertaining to that group. The resulting code is shown to be robust, and to produce accurate results when compared with exact solutions of selected fluid dynamic problems involving surface tension

A Deus, que me protege e ilumina o meu caminho nesta missão, que é a vida. Ao Prof. Castelo pela orientação dedicada, pela ativa participação, pela paciência e pelos conhecimentos transmitidos durante todo o decorrer deste trabalho. Aos meus pais, Nelson e Ana, pelo carinho, incentivo e apoio em todos os momentos da minha vida. Ao meu noivo Armando Luis pelo amor, carinho e compreensão, que soube suportar a minha ausência e me confortar nos momentos difíceis. À minha família pelo apoio e incentivo neste período de muitas ausências e em especial à minha avó Laudina, pelas orações. Ao pessoal do LCAD e do grupo de Análise Numérica, pelas constantes sugestões e pela amizade. Em especial ao prof. Norberto, ao prof. Murilo, ao prof. Armando, ao prof. Gustavo e ao prof. Poti, pelos ensinamentos. À professora Ângela, do centro cultural, pelas aulas de inglês e por nossa amizade. Aos meus professores de graduação do departamento de matemática da UFSCar, em especial ao prof. Ivo Machado da Costa, que abriu as portas para a realização deste trabalho. À amiga Christiane pela grande amizade desde a época da graduação. À Juliana, Aninha e Rodrigo, pela colaboração nos estudos, pelas inúmeras dúvidas esclarecidas e principlamente pela amizade.

This paper introduces the concept of digital planar surfaces and corresponding Morse operators. These operators offer a novel and powerful method for construction and de-construction of such surfaces in a way that global topological control of the resulting object is always maintained. In that respect, this paper offers a complete pixel characterization tool. Image handling is a natural application for such approach. We present a novel fast algorithm for image segmentation using Morse operators for digital planar surfaces. It classifies as a region growing technique with added topological control and is extremely useful for applications that need proper object description. Results from real data are stimulating, and show that the segmentation algorithm compares very well with other methods. The topological approach also forms a base for future expansion to applications such as volume segmentation.