Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-10-29
Physics
Condensed Matter
Statistical Mechanics
20 pages with 12 figs. Accepted in the Physica A
Scientific paper
10.1016/j.physa.2004.08.076
The Cahn-Hilliard 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 an 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 Cahn-Hilliard with two improvements: a splitting potential into a implicit and explicit in time part and a 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.
de Mello Evandro V. L.
Silveira Filho Otton Teixeira da
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