Abstract
The Swift–Hohenberg equation accurately models the formation and evolution of patterns in a wide range of systems. However, in the field of fluid dynamics, two particular patterns arise during the Rayleigh-Benard convection, rolls and hexagons, and the formation of both has been simulated in this work. The Swift–Hohenberg (S–H) equation is a nonlinear partial differential equation of fourth order, and through an implicit finite differences method it has been numerically solved. A set of snapshots of the evolution of these patterns is shown.
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