Energy Stable Numerical Method for the TDGL Equation with the Reticular Free Energy in Hydrogel

Energy Stable Numerical Method for the TDGL Equation with the Reticular Free Energy in Hydrogel

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.

Author Details

Dong Liao

Hui Zhang

Zhengru Zhang

  1. An Energy Stable Finite Element Scheme for the Three-Component Cahn–Hilliard-Type Model for Macromolecular Microsphere Composite Hydrogels

    Yuan, Maoqin

    Chen, Wenbin

    Wang, Cheng

    Wise, Steven M.

    Zhang, Zhengru

    Journal of Scientific Computing, Vol. 87 (2021), Iss. 3

    https://doi.org/10.1007/s10915-021-01508-w [Citations: 30]