TY - JOUR

T1 - Numerical solution of the Swift-Hohenberg equation in two dimensions

AU - Xi, Hao wen

AU - Viñals, Jorge

AU - Gunton, J. D.

PY - 1991/9/15

Y1 - 1991/9/15

N2 - 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.

AB - 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.

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U2 - 10.1016/0378-4371(91)90173-A

DO - 10.1016/0378-4371(91)90173-A

M3 - Article

AN - SCOPUS:0004866862

VL - 177

SP - 356

EP - 365

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1-3

ER -