Solução das equações de Saint Venant em uma e duas dimensões usando o Método das Características

• Ano de defesa: 2012
• Autor(a) principal: Lobeiro, Adilandri Mércio
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Paraná; Campo Mourao; Programa de Pós-Graduação em Métodos Numéricos em Engenharia
• Palavras-chave em Português: Ondas (Física); Diferenças finitas; Equações diferenciais; Equação de onda; Waves; Finite differences; Differential equations; Wave equation
• Link de acesso: http://repositorio.utfpr.edu.br/jspui/handle/1/769

Basing on the theory of the kinematics of the fluid is achieved via the Reynolds transport theorem, deductions required to obtain the Saint Venant equation in one and two dimensions, although such equations are linearized, which allows to obtain wave equations in one and two dimensions. To solve these equations, this text discusses the consecrated Method of Characteristics, detailing it. It should be noted that for the two-dimensional case met the Pseudo characteristics. By means of this method and with the aid of the software maple two known solution of the wave equation is obtained from Equation telegraph in case of one dimension, and to evaluate the vibration of a rectangular diaphragm in the case of two-dimensional . Furthermore, the method of characteristics is applied to obtain the slopes of Characteristic Curves and Riemann invariants in order to solve the Saint Venant equations in one and two dimensions, in each of the situations a case study was approached in to expose the theory developed. For the one dimensional case we analyzed the flow of water in a rectangular channel and evaluating the speed at specific positions depth of the channel length and time instants pre-set, making it possible to estimate these values at any point in the channel by through a twice continuously differentiable function which was obtained by interpolating the type Natural Cubic Spline. For the case in two dimensions, a problem of emptying a two-dimensional reservoir was analyzed using the Saint Venant equation, yielding results such as the depth and speed in both directions to specific time instants and positions prefixed length, and width of the reservoir, these results were compared with the data obtained by the already established Explicit Finite Difference Method. Importantly, for the process of solving each of the equations, one Maplet was designed and programmed in order to illustrate and evaluate numerically and graphically the results obtained by each method.