Aplicação de autômato celular para fluidos

Abstract

The Amazon Region keeps 70% of all fresh water of Brazil, however, the man’s presence is responsable for pollution in our rivers and, nowadays, it is increasing the world interest in the nature preservation. Facts like these led scientists to creat computational modelling techniques capable to preview the man’s impacts in the nature. However, it is not so easy, per exemple, to model the flow of a river with Amazon´s rivers dimensions. It is of crucial importance in the Amazon Region, researchers involved in giving answers in case of environmental impacts that can come to destroy this world patrimony. To study a river flow, it is necessary to solve the equations that describe the movement of liquids and gases, the Equations of Navier-Stokes associated the Equation of the Continuity that are no-linear partial differential equations. Cellular automata models allow the simulation of complex systems, and their applications in fluids are known as "lattice gas automata", one computational technique that will be used in this work to observe the paths of a fluid through barriers. Lattice gas model of is an abstraction, at a microscopic scale, of a fluid. It is based on the idea that if we reproduce the fundamental conservation laws and symmetries associated with fluids, at a microscopic level, then we can model, correctly, the behavior of the fluid at a macroscopic level. In this model, the particles occupy a lattice, possess discrete velocities and following deterministic rules according to the physical laws; this work uses a two-dimensional hexagonal lattice, because its symmetry is more closely relatedtoacontinuumfluid. Inthisworkwesimulatedthetwo-dimensionalfluidmotion, in a "L" shape container , without or with barrier, imitating the form of the rivers of the North of Brazil(to see Fig.0.1), with the objective of obtaining a way to foresee the behavior of the rivers in situations of environmental impacts. Themodelproposedhereissimple,however,itledtogoodresultsofthefluidbehavior and,ifgottenbetter,canbeofalotofutilityforthestudyofrivermotion. Wedidn’tfind on the literature any work with a "L" shape container for comparing withour results. It was presented, just, a study of the fluids phenomena expected for this path.