Abstract
The numerical simulation of flows with topological changes is quite challenging, being approached in the literature by different techniques, highlighting fixed mesh methods, generally based on immersed boundary techniques, and particle-based methods, generally based on a Lagrangian description of the flow. One approach that has proven to be efficient is the particle and finite element method (PFEM), which combines the concepts of particle methods with the finite element method. In this context, this work deals with the development and implementation of techniques for simulating two-phase flows with free surface and topological changes in an alternative formulation of PFEM, where instead of velocities as nodal parameters, particle positions are used. Initially, the domains of the two fluids are represented by a cloud of particles to which the physical characteristics of the fluid they represent are attributed, as well as the initial conditions. A mesh of finite elements is built on this particle cloud to solve the equation of motion in Lagrangian description, with the physical characteristics, as well as the velocity and pressure fields, being interpolated by the shape functions of the finite elements. To avoid large distortions, and also mesh entanglement, at each step this mesh is destroyed and a new mesh is built. Delaunay triangulation is used to construct the mesh, together with the alpha-shape method to define the contours, together with a particle relocation technique that must guarantee the quality of the mesh (avoid extremely small elements or elements with a very small volume ), as well as ensuring the conservation of the number of particles of each fluid. This formulation is tested for cases of free surface flows, such as sloshing in reservoirs, taking into account the water-air interaction, and the results are compared with results from the literature.
Published Version
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