Numerical solution of the Swift-Hohenberg equation in two dimensions

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

Physica A: Statistical Mechanics and its Applications, 1991, vol. 177, issue 1, 356-365

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.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:177:y:1991:i:1:p:356-365

DOI: 10.1016/0378-4371(91)90173-A

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