Year: 2017
Author: Dong Liao, Hui Zhang, Zhengru Zhang
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 1 : pp. 37–51
Abstract
Here we focus on the numerical simulation of the phase separation about macromolecule microsphere composite (MMC) hydrogel. The model is based on time-dependent Ginzburg-Landau (TDGL) equation with the reticular free energy. An unconditionally energy stable difference scheme is proposed based on the convex splitting of the corresponding energy functional. In the numerical experiments, we observe that simulating the whole process of the phase separation requires a considerably long time. We also notice that the total free energy changes significantly in initial stage and varies slightly in the following time. Based on these properties, we apply the adaptive time stepping strategy to improve the computational efficiency. It is found that the application of time step adaptivity can not only resolve the dynamical changes of the solution accurately but also significantly save CPU time for the long time simulation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1607-m2014-0109
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 1 : pp. 37–51
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: TDGL equation Unconditionally energy stable scheme Adaptive time-stepping method Phase transition.