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Numerical solution of the Swift-Hohenberg equation in two dimensions

Author

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  • Xi, Hao-wen
  • Viñals, Jorge
  • Gunton, J.D.

Abstract

The Swift-Hohenberg equation with either a stochastic or a constant forcing term has been solved numerically in two spatial dimensions. The parameters that enter the equation have been chosen to match the experiments on Rayleigh-Bénard convection by Meyer et al. [C.W. Meyer, G. Ahlers and D.S. Cannell, Phys. Rev. Lett. 59 (1987) 1577]. Our numerical results for the convective heat current as a function of time fit the experiments well (the fitting parameter is the amplitude of the forcing term). We find a value of F = 5.52 × 10−6 for the stochastic case, compared to Fth = 1.06 × 10−10, the value obtained from fluctuation theory. The structure of the convective pattern also depends on the type of forcing considered. A constant forcing induces a roll-like pattern that reflects the geometry of the sidewalls. A stochastic forcing is seen to induce a random, cellular pattern.

Suggested Citation

  • Xi, Hao-wen & Viñals, Jorge & Gunton, J.D., 1991. "Numerical solution of the Swift-Hohenberg equation in two dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 177(1), pages 356-365.
    • Handle: RePEc:eee:phsmap:v:177:y:1991:i:1:p:356-365
    DOI: 10.1016/0378-4371(91)90173-A
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    Cited by:

    1. Tokuyama, Michio & Enomoto, Yoshihisa, 1994. "On the theory of late-stage phase separation in off-critically quenched binary systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 204(1), pages 673-692.

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