Numerical approach to pattern selection in a model problem for Bénard convection in finite fluid layer
Keywords:
difference schemes, higher-order diffusion equations, nonlinearity, operator splitting, pattern selection, surface-tension driver convectionAbstract
Long wave-length pattern formation is studied by means of numerical integration of a fourth-order in space nonlinear evolution equation subjected to Dirichlet laeral boundary conditions. Computationally efficient implicit difference scheme and algorithm are devised emplouying the method of operator splitting.
The case of Bénard convection in Boussinesq limit is considered. For different sets of the parameters different convective planforms are found: a pattern of hexagons (