Numerical study of the Cahn–Hilliard equation in one, two and three dimensions

E.V.L. de Mello and Otton Teixeira da Silveira Filho

Physica A: Statistical Mechanics and its Applications, 2005, vol. 347, issue C, 429-443

Abstract: The Cahn–Hilliard (CH) equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff and the difficulty to solve it numerically increases with the dimensionality and therefore, there are several published numerical studies in one dimension (1D), dealing with different approaches, and much fewer in two dimensions (2D). In three dimensions (3D) there are very few publications, usually concentrate in some specific result without the details of the used numerical scheme. We present here a stable and fast conservative finite difference scheme to solve the CH with two improvements: a splitting potential into an implicit and explicit in time part and the use of free boundary conditions. We show that gradient stability is achieved in one, two and three dimensions with large time marching steps than normal methods.

Keywords: Phase separation; Finite-difference methods; Spatially inhomogeneous structures (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:347:y:2005:i:c:p:429-443

DOI: 10.1016/j.physa.2004.08.076

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