International Scientific Journal

Authors of this Paper

External Links


A collocation Fourier scheme for Swift-Hohenberg equation based on the convex splitting idea is implemented. To ensure an efficient numerical computation, we propose a general framework with linear iteration algorithm to solve the non-linear coupled equations which arise with the semi-implicit scheme. Following the contraction mapping theorem, we present a detailed convergence analysis for the linear iteration algorithm. Various numerical simulations, including verification of accuracy, dissipative property of discrete energy and pattern formation, are presented to demonstrate the efficiency and the robustness of proposed method.
PAPER REVISED: 2018-09-20
PAPER ACCEPTED: 2018-11-15
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 3, PAGES [S669 - S676]
  1. Swift, J., Hohenberg,P. C., Hydrodynamic fluctuations at the convective instability, Phys. Rev. A,15(1977), 1, pp. 319-328
  2. Vanag,V. K., Epstein,I. R., Stationary and oscillatory localized patterns, and subcritical bifurcations, Phys. Rev. Lett., 92(2004), 12, pp. 1-4
  3. Oswald, P., et al., Static and dynamic properties of cholesteric fingers in electric field, Physics Reports, 337(2000), 1, pp. 67-96
  4. Ribiere, P., Oswald, P., Nucleation and growth of cholesteric fingers under electric field, Journal De Physique, 51(1990), 16, pp.1703-1720
  5. Cheng, M., Warren,J. A., An efficient algorithm for solving the phase field crystal model, J. Comput. Phys., 227(2008), 12, pp. 6241-6248
  6. Backofen, R., et al., Nucleation and growth by a phase field crystal (PFC) model, Phil. Mag. Lett., 87(2007), 11, pp. 813-820
  7. Cheng, K., et al., A Fourier pseudospectral method for the "good" Boussinesq equation with second-order temporal accuracy, Numer. Meth. Partial Diff. Eq., 31(2015), 1, pp. 202-224
  8. Kang, X., et al., An efficient finite difference scheme for the 2D sine-Gordon equation, J. Nonlinear Sci. Appl.,10 (2017), 1, pp. 2998-3012
  9. Baskaran, A., et al., Energy stable and efficient finite difference nonlinear multigrid schemes for the modified phase field crystal equation, J. Comput. Phys., 250(2013), 10, pp. 270-292
  10. Cheng, K., et al., A second-order, weakly energy-stable pseudo-spectral scheme for the Cahn-Hilliard equation and its solution by the homogeneous linear iteration method, J. Sci. Comput., 69(2016), 3, pp. 1083-1114
  11. Cheng, K., et al., An energy stable fourth order finite difference scheme for the Cahn-Hilliard equation, J. Comput. Appl. Math.,1 (2019), 5, pp. 1-22.
  12. Xue, Y., et al.,Evaluation of the Non-Darcy Effect of Water Inrush from Karst Collapse Columns by Means of a Nonlinear Flow Model, Water,10 (2018), 9, pp. 1234
  13. Feng, W., et al., Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms, J. Comput. Phys., 334(2016), 1, pp. 45-67
  14. Gomez, H., NogueiraX., A new space-time discretization for the Swift-Hohenberg equation that strictly respects the Lyapunov functional, Commun. Nonlinear Sci. Numer. Simulat.,17(2012), 12, pp. 4930-4946
  15. Lloyd, D., Sandstede B., Localized radial solutions of the Swift-Hohenberg equation, Nonlinearity, 22(2009), 2, pp. 485-524

© 2020 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence