Simulação da Equação de Burgers Invíscida e Estocástica

• Autor(a) principal: dos Santos Vianna Jr., Ardson
• Data de Publicação: 2024
• Outros Autores: Gomes, Rafael Giglio, Reis, M
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Revista Interdisciplinar de Pesquisa em Engenharia
• Texto Completo: https://periodicos.unb.br/index.php/ripe/article/view/52165
• topic: EDP estocástica; Python; Trajetória amostral

The Burgers equation is the first step in solving the Navier–Stokes equation, which is fundamental one in the study of computational fluid dynamics. Even the inviscid version of the Burgers equation results in a nonlinear partial differential equation, which should be solved with the proper approach. In this work, the inviscid and stochastic Burgers equation is solved. Euler's explicit method was used to integrate time, generating a march algorithm. For the space, the backward finite difference formula was used. Randomness was inserted through a Wiener process in time. The parameters evaluated here are part of the Aksan and Özdeş article (2004), that was used to verify the deterministic model. By using the approach here described, the nonlinearity and randomness were resolved, allowing the progression to the solution of more complex models. The simulation result are sample paths that represent the velocity profiles with stochastic oscillations, a physical phenomenon that occurs in nature.