Triple junction benchmark for multiphase-field models combining capillary and bulk driving forces
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Due to their ability to handle complex multiphase problems, multiphase-field and multi-order parameter methods have become increasingly popular. Since their emergence, several formulations and modifications have been published, but a comprehensive comparison has remained elusive. In this work, we introduce a well-defined triple junction setup in terms of initial and boundary conditions with a static and a steady-state subproblem. The triple junction is of particular interest for validation purposes, as it allows for the evaluation of multi-phase extensions from the two-phase case, while the simulation setup itself is relatively simple. Metrics such as the total energy of the system and the dihedral angle at the interface are derived from analytical considerations and compared to numerical results from simulation studies. Additionally, the effect of a bulk driving force on the phase transformation velocity and triple junction dynamics is investigated analytically and with simulation studies. The benchmark allows to quantify the performance of various model formulations with respect to the sharp interface solution and, thereby, provides guidelines for the selection of a suitable, problem-specific model formulation and the development of new models.
