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Numerical Solution of the Swift–Hohenberg Equation

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Experimental and Computational Fluid Mechanics

Part of the book series: Environmental Science and Engineering ((ENVENG))

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-Bénard 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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Acknowledgments

We want to express our gratitude to Prof. Pablo de la Mora for his invaluable help and DGAPA-UNAM for their financial support under grant PAPIIT-IN110210.

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Authors and Affiliations

  1. Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, C.P.04510, Distrito Federal, México

    S. Sánchez Pérez-Moreno, S. Ruiz Chavarría & G. Ruiz Chavarría

Authors
  1. S. Sánchez Pérez-Moreno
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  2. S. Ruiz Chavarría
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  3. G. Ruiz Chavarría
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Corresponding author

Correspondence to S. Sánchez Pérez-Moreno .

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Editors and Affiliations

  1. Instituto Nacional des Investigaciones Nucleares, Mexico, Mexico

    Jaime Klapp

  2. Departamento de Ciencias Básicas, Unviersidat Autonóma Metropolitana-Azcapotzalco, Mexico, Mexico

    Abraham Medina

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Sánchez Pérez-Moreno, S., Ruiz Chavarría, S., Ruiz Chavarría, G. (2014). Numerical Solution of the Swift–Hohenberg Equation. In: Klapp, J., Medina, A. (eds) Experimental and Computational Fluid Mechanics. Environmental Science and Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-00116-6_36

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