Junction dynamics in phase-field simulations vis-à-vis asymptotics predictions : A beginning study

Abstract

An ideal situation in phase-field methodology is when realistic evolution dynamics can be simulated at much larger interface widths. Asymptotic analysis, at best, can only help half address the challenge. It might give insights for making model adjustments so as to capture the appropriate sharp-interface description up to various orders of accuracy. However, this still is insufficient to conclude if artificial enlargement of interfacial thickness to desirable degree is permissible. Laborious numerical tests and crosschecks have to be performed to find it out. The current work will emerge to stand as a classic example for such a scenario. It is seen that sensitivity to modeling choices is more pronounced in the case of evolution of junctions than it is anywhere else. In particular, we noticed that interfacial mobility interpolating forms or formulations can put up severe restrictions on the required interface widths for reproducing close to converged sharp-interface behaviors. To make things worse, this is highly system dependent, i.e., the same material system considered in a different setup, or the same setup when considered for different material systems can require a change in mobility formulation for faster recovery of the limiting dynamics. Also, it is found that the traditional recipe popularly adopted for carrying out interface-width reduction studies is unsustainable and has to be replaced by a costlier routine.