Utilização do método da hidrodinâmica de partículas suavizadas aplicado à resolução de problemas eletromagnéticos

Abstract

The solution of partial differential equations has an important role in thecomputational simulation of engineering problems. Many numerical methods to solve such kind of problems were developed through decades. Although there exist precise and stable methods nowadays, the traditional methods still require a lot of human effort, specially in what refers to mesh generation. Meshes are a building block for such traditional methods. With the advent of new methods where meshes are no longer necessary, intensive research have being developed as a tentative of making them applicable to any kind of problems, always trying to reach better precision and speed on simulations without human interaction in the process. In this work it is presented and studied one of the first meshless methods which is known as Smoothed Particle Hydrodynamics. This method was created for the simulation of fluid hydrodynamics but it is now also used for other kind of engineering problems. Relevant aspects of the method such as the consistency order or the imposition of boundary conditions are discussed and a computacional parallel algorithm is proposed. In order to validate the method's formulation, the results obtained for simple problems using a parallel computacional implementation are presented. The eficiency of the parallelization of the method is verified to attest its capacity for fast solution of large scale problems. Finally, it is also pointed out some dificulties that arise when using the Smoothed Particle Hydrodynamics