Eventos Anais de eventos
COBEM 2019
25th International Congress of Mechanical Engineering
Pattern Formation Survey on Non Uniformly Forced Swift-Hohenberg Equation
Submission Author:
Daniel Coelho , RJ
Co-Authors:
Daniel Coelho, José da Rocha Miranda Pontes, Norberto Mangiavacchi
Presenter: Daniel Coelho
doi://10.26678/ABCM.COBEM2019.COB2019-0775
Abstract
The present paper considers a generalized nonlinear diffusion equation known as the Swift-Hohenberg (SH) equation. Applications of this equation include the study of pattern formation in physical problems outside equilibrium, described by phase field models, such as the hydrodynamic instability of a fluid under thermal convection or even the structural evolution of nanostructured copolymers. Numerical solutions of the SH equation present patterns with a large number of topological defects, e.g., grain boundaries, dislocations and disclinations ; so computational modelling of such mesoscopic characteristics can help us to understand, explain and predict macroscopic properties of an extended system of interest. A finite-difference semi-implicit time splitting scheme is employed on the discretization of the governing equation in two dimensions. Simulations were performed with nonuniform forcings such as ramped and gaussian distributions. Bidimensional rolls patterns (stripes) were obtained from random initial conditions and numerical stability is verified. Distinct structure orientation and a subcritical effect can be observed for miscellaneous domain sizes and forcings.
Keywords
Swift-Hohenberg Equation, Pattern Formation, Topological Defects, Implicit Methods, Finite Difference Methods
