Numerical approximation of oscillating Turing patterns in a reaction-diffusion model for electrochemical material growth

Abstract

In this paper a reaction-diffusion system for electrochemical material growth processes is considered, including an external sinusoidal forcing term for the PDE equation describing the morphology of the electrodeposit surface profile. The numerical approximation by the Alternating Direction Implicit (ADI) method based on Extended Central Difference Formulas (ECDF) of order p = 4 in space is applied to investigate the way the variation of the frequency of the superimposed voltage sinusoid affects Turing pattern scenarios corresponding to steady state solutions of the unforced model. The ADI-ECDF method, introduced in [20] for the approximation of Turing patterns in the unforced case, is shown to be efficient from the computational point of view also to track oscillating Turing patterns for long-time simulations. In particular, the proposed method allows to identify a critical frequency range where the ripple effect arises, that is spots & worms patterns, related to the buildup of roughness in the material growth process, are suppressed and spatially homogeneous steady state solutions are attained. Such results have been validated by comparison with original experimental results on the growth of silver chloride films. © 2012 American Institute of Physics.