Volume 11, Issue 4
An Adaptive Time-stepping Strategy for the Cahn-Hilliard Equation

Zhengru Zhang and Zhonghua Qiao


Commun. Comput. Phys., 11 (2012), pp. 1261-1278.

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  • Abstract

This paper studies the numerical simulations for the Cahn-Hilliard equation which describesaphase separationphenomenon. The numericalsimulation of the Cahn-Hilliardmodel needs verylong time toreachthe steadystate, andthereforelarge time-stepping methods become useful. The main objective of this work is to construct the unconditionally energy stable finite difference scheme so that the large time steps can be used in the numerical simulations. The equation is discretized by the central difference scheme in space and fully implicit second-order scheme in time. The proposed scheme is proved to be unconditionally energy stable and mass-conservative. An error estimate for the numerical solution is also obtained with second order in both space and time. By using this energy stable scheme, an adaptive time-stepping strategy is proposed, which selects time steps adaptively based on the variation of the free energy against time. The numerical experiments are presented to demonstrate the effectiveness of the adaptive time-stepping approach.

  • History

Published online: 2012-04

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