Numerical Study of Defects in Swift-Hohenberg Dynamics

The present paper considers a generalized nonlinear diffusion equation known as the Swift-Hohenberg (SH) equation, applied fo some physical problems outside equilibrium. Numerical solutions of the SH equation present patterns with a large number of topological defects. A semi-implicit finite difference scheme with temporal discretization of first and second orders was implemented in the discretization of the governing equation in 2D. Simulations were performed with parameters found in the literature and some of them with a quadratic nonlinearity. Bidimensional rolls patterns, such as hexagonals and stripes were obtained from random initial conditions for certain values of the bifurcation parameter and the coefficient associated to the quadratic nonlinearity. Numerical results obtained with schemes of both orders show good agreement with the literature, and defects dynamics also responds to the implemented numerical approximation.