A space-time adaptivity scheme for the Cahn-Hilliard equation

• Ano de defesa: 2019
• Autor(a) principal: Barros, Gabriel Freguglia
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal do Rio de Janeiro; Brasil; Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia; Programa de Pós-Graduação em Engenharia Civil; UFRJ
• Palavras-chave em Português: Phase-field modelling; Cahn-Hilliard equation; Space-time adaptivity; CNPQ::ENGENHARIAS::ENGENHARIA CIVIL
• Link de acesso: http://hdl.handle.net/11422/14009

In this study, we propose a space-time adaptivity scheme for the Cahn-Hilliard equation. We evaluate two error indicators for the spatial adaptivity scheme coupled with the bissection method for refinement, while the temporal adaptivity scheme is recast under the linear feedback control theory. We consider an error estimation in time that extrapolates the solution obtained from an energy-stable time marching scheme, and three time step controllers: a simple integral controller, a complete Proportional-Integral-Derivative controller, and the predictive controller known as PC11. We assess the performance of the adaptive schemes for different physical contexts for the Cahn-Hilliard equation, such as the Navier-Stokes-Cahn-Hilliard coupling and the nonlocal Cahn-Hilliard equation, simulating different physics and time scales. We validate our strategy with benchmark simulations in the literature and evaluate the performance gain for each case.