A fast and high accuracy numerical simulation algorithm of the polymer spherulite at the mesoscale Level

摘要

In the multiscale numerical simulation of polymer crystallization during the processing period, flow and temperature of the polymer melt are simulated on the macroscale level, while nucleation and growth of the spherulite are simulated at the mesoscale level. As a part of the multiscale simulation, the meso-simulation requires a fast solving speed because the meso-simulation software must be run several times in every macro-element at each macro-step. Meanwhile, the accuracy of the calculation results is also very important. It is known that the simulation geometry of crystallization includes planar (2D) and three-dimensional space (3D). The 3D calculations are more accurate but more expensive because of the long CPU time consumed. On the contrary, 2D calculations are always much faster but lower in accuracy. To reach the desirable speed and high accuracy at the same time, an algorithm is presented, in which the Delesse law coupled with the Monte Carlo method and pixel method are employed to simulate the nucleation, growth, and impingement of the polymer spherulite at the mesoscale level. Based on this algorithm, a software is developed with the Visual C++ language, and its numerical examples' results prove that the solving speed of this algorithm is as fast as the 2D classical simulation and the calculation accuracy is at the same level as the 3D simulation.