High efficiently numerical simulation of the TDGL equation with reticular free energy in hydrogel
This work provides efficient numerical methods for long-time simulation of phase separation in hydrogels, a domain-specific problem in materials science.
The authors developed L2 stable numerical schemes and an adaptive time-stepping strategy for simulating phase separation in MMC hydrogels using the TDGL equation, achieving significant CPU time savings while maintaining accuracy.
In this paper, we focus on the numerical simulation of phase separation about macromolecule microsphere composite (MMC) hydrogel. The model equation is based on Time-Dependent Ginzburg-Landau (TDGL) equation with reticular free energy. We have put forward two $L^2$ stable schemes to simulate simplified TDGL equation. In numerical experiments, we observe that simulating the whole process of phase separation requires a considerably long time. We also notice that the total free energy changes significantly in initial time and varies slightly in the following time. Based on these properties, we introduce an adaptive strategy based on one of stable scheme mentioned. It is found that the introduction of the time adaptivity cannot only resolve the dynamical changes of the solution accurately but also can significantly save CPU time for the long time simulation.