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In this paper, we focus on the numerical simulation of phase separation aboutmacromolecule microsphere composite (MMC) hydrogel. The model equation is basedon Time-Dependent Ginzburg-Landau (TDGL) equation with reticular free energy.We have put forward two $L^2$ stable schemes to simulate simplified TDGLequation. In numerical experiments, we observe that simulating the wholeprocess of phase separation requires a considerably long time. We also noticethat the total free energy changes significantly in initial time and variesslightly in the following time. Based on these properties, we introduce anadaptive strategy based on one of stable scheme mentioned. It is found that theintroduction of the time adaptivity cannot only resolve the dynamical changesof the solution accurately but also can significantly save CPU time for thelong time simulation.

High efficiently numerical simulation of the TDGL equation with reticular free energy in hydrogel